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1.
We prove induced Ramsey theorems in which the monochromatic induced subgraph satisfies that all members of a prescribed set
of its partial isomorphisms extend to automorphisms of the colored graph (without requirement of preservation of colors).
We consider vertex and edge colorings, and extensions of partial isomorphisms in the set of all partial isomorphisms between
singletons as considered by Babai and Sós (European J Combin 6(2):101–114, 1985), the set of all finite partial isomorphisms as considered by Hrushovski (Combinatorica 12(4):411–416, 1992), Herwig (Combinatorica 15:365–371, 1995) and Herwig-Lascar (Trans Amer Math Soc 5:1985–2021, 2000), and the set of all total isomorphisms. We observe that every finite graph embeds into a finite vertex transitive graph
by a so called bi-embedding, an embedding that is compatible with a monomorphism between the corresponding automorphism groups. We also show that every
countable graph bi-embeds into Rado’s universal countable graph Γ. 相似文献
2.
V. D. Derech 《Ukrainian Mathematical Journal》2012,63(9):1390-1399
For a semigroup S, the set of all isomorphisms between the subsemigroups of the semigroup S with respect to composition is an inverse monoid denoted by PA(S) and called the monoid of local automorphisms of the semigroup S. The semigroup S is called permutable if, for any couple of congruences ρ and σ on S, we have ρ ∘ σ = σ ∘ ρ. We describe the structures of a finite commutative inverse semigroup and a finite bundle whose monoids of local automorphisms
are permutable. 相似文献
3.
Amal AlAli 《代数通讯》2017,45(11):4667-4678
4.
Nándor Sieben 《Czechoslovak Mathematical Journal》2008,58(3):683-692
The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms
of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid.
The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to
the original groupoid. 相似文献
5.
V. D. Derech 《Ukrainian Mathematical Journal》2005,57(4):565-570
We describe the structure of any congruence of a permutable inverse semigroup of finite rank.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 469–473, April, 2005. 相似文献
6.
A. V. Rukolaine 《Journal of Mathematical Sciences》1982,20(6):2657-2664
For elements of a finite inverse semigroup, an equivalence relation called p-conugacy is introduced. It is proved that for any matrix representation of a finite inverse semigroup the values of the character of the representation are equal on p-conjugate elements. The number of inequivalent irreducible matrix representations of a finite inverse semigroup over the field of complex numbers is equal to the number of classes of p-conjugate elements.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 71, pp. 207–215, 1977. 相似文献
7.
A. S. Oliinyk 《Mathematical Notes》1998,63(2):215-224
It is established that the subset of freek-generated subsemigroups of the semigroup of all automaton transformations over a finite alphabet is a second category set
(in the sense of the Baire category approach) in the set of allk-generated subsemigroups. A continuum series of pairs of automaton transformations each of which generates a free semigroup
of rank two is indicated. A criterion is established for this semigroup to be a finite-automaton group.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 248–259, February, 1998.
The author wishes to express his deep gratitude to Professor V. I. Sushchans'kii for permanent help and attention to the research.
This research was partially supported by the ISSEP under grant No. GSU 051341. 相似文献
8.
For each [directed] graph we construct an inverse semigroup. Our main application is a simple proof of the characterization of partially ordered sets ofJ-classes of finite semigroups, and some generalizations; our proof avoids using the inductive construction of the previous method by one of the authors [4]. For a connected graph in which each vertex has index at least two, our construction gives a congruence free inverse semigroup. In the final section we describe how a slight modification bf the construction yields the polycyclic monoids. 相似文献
9.
It is proved that any pseudovariety of finite semigroups generated by inverse semigroups, the subgroups of which lie in some
proper pseudovariety of groups, does not contain all aperiodic semigroups with commuting idempotents. In contrast we show
that every finite semigroup with commuting idempotents divides a semigroup of partial bijections that shares the same subgroups.
Finally, we answer in the negative a question of Almeida as to whether a result of Stiffler characterizing the semidirect
product of the pseudovarieties ofR-trivial semigroups and groups applies to any proper pseudovariety of groups. 相似文献
10.
We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups,
particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of
finite transformations I
λ
n
of the rank ≤
n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. We also derive related
results about the nonexistence of (partial) compactifications of classes of semigroups that we consider. 相似文献
11.
Yingdan Ji 《代数通讯》2013,41(12):5149-5162
Let S be a finite orthodox semigroup or an orthodox semigroup where the idempotent band E(S) is locally pseudofinite. In this paper, by using principal factors and Rukolaǐne idempotents, we show that the contracted semigroup algebra R0[S] is semiprimitive if and only if S is an inverse semigroup and R[G] is semiprimitive for each maximal subgroup G of S. This theorem strengthens previous results about the semiprimitivity of inverse semigroup algebras. 相似文献
12.
V. A. Yurko 《Mathematical Notes》1998,64(1):121-132
The inverse spectral problem for Sturm-Liouville differential operators on a finite interval is studied for an arbitrary and finite number of regular singular points inside the interval. A uniqueness theorem is proved; necessary and sufficient conditions and a procedure for the solution of the inverse problem are obtained.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 143–156, July, 1998.This research was supported by the Ministry of Education (KTsFE) under grant No. 96-1.7-4 and by the Russian Foundation for Basic Research under grant No. 97-01-00566. 相似文献
13.
Pedro V. Silva 《代数通讯》2013,41(6):2482-2494
An inverse semigroup S is a Howson inverse semigroup if the intersection of finitely generated inverse subsemigroups of S is finitely generated. Given a locally finite action θ of a group G on a semilattice E, it is proved that E*θG is a Howson inverse semigroup if and only if G is a Howson group. It is also shown that this equivalence fails for arbitrary actions. 相似文献
14.
In this paper we study sub-semigroups of a finite or an infinite zero-divisor semigroup S determined by properties of the zero-divisor graph Γ(S). We use these sub-semigroups to study the correspondence between zero-divisor semigroups and zero-divisor graphs. In particular, we discover a class of sub-semigroups of reduced semigroups and we study properties of sub-semigroups of finite or infinite semilattices with the least element. As an application, we provide a characterization of the graphs which are zero-divisor graphs of Boolean rings. We also study how local property of Γ(S) affects global property of the semigroup S, and we discover some interesting applications. In particular, we find that no finite or infinite two-star graph has a corresponding nil semigroup. 相似文献
15.
Bernhard Herwig 《Israel Journal of Mathematics》1998,107(1):93-123
Theorem:Let A be a finite K
m
-free graph, p
1
, …, p
n
partial isomorphisms on A. Then there exists a finite extension B, which is also a K
m
-free graph, and automorphisms f
i
of B extending the p
i
.
A paper by Hodges, Hodkinson, Lascar and Shelah shows how this theorem can be used to prove the small index property for the
generic countable graph of this class. The same method also works for a certain class of continuum many non-isomorphic ω-categorical
countable digraphs and more generally for structures in an arbitrary finite relational language, which are built in a similar
fashion. Hrushovski proved this theorem for the class of all finite graphs [Hr]; the proof presented here stems from his proof.
Supported by EC-grant ERBCHBGCT 920013. 相似文献
16.
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of self-adjoint semigroups of partial isometries. We obtain a general structure result showing that every self-adjoint semigroup of partial isometries consists of “generalized weighted composition” operators on a space of square-integrable Hilbert-space valued functions. If the semigroup is finitely generated then the underlying measure space is purely atomic, so that the semigroup is represented as “zero-unitary” matrices. The same is true if the semigroup contains a compact operator, in which case it is not even required that the semigroup be self-adjoint. 相似文献
17.
Vítor H. Fernandes 《Semigroup Forum》2008,76(3):579-583
In this note we characterize the least positive integer n such that there exists an idempotent-separating homomorphism from a finite block-group S into the monoid of all partial transformations of a set with n elements. In particular, as for a fundamental semigroup S this number coincides with the smallest size of a set for which S can be faithfully represented by partial transformations, we obtain a generalization of Easdown’s result established for
fundamental finite inverse semigroups.
The author gratefully acknowledges support of FCT and FEDER, within the project POCTI-ISFL-1-143 of CAUL, and the fellowship
SFRH/BSAB/244/2001. 相似文献
18.
A. V. Zavarnitsine 《Algebra and Logic》2006,45(4):220-231
We obtain the first example of an infinite series of finite simple groups that are uniquely determined by their prime graph
in the class of all finite groups. We also show that there exist almost simple groups for which the number of finite groups
with the same prime graph is equal to 2.
Supported by RFBR grant No. 05-01-00797, and by SB RAS Young Researchers Support grant No. 29 and Integration project No.
2006.1.2.
__________
Translated from Algebra i Logika, Vol. 45, No. 4, pp. 390–408, July–August, 2006. 相似文献
19.
B. V. Novikov 《Journal of Mathematical Sciences》1994,72(4):3223-3225
The structure of additive semigroups generated by finite sets of n -dimensional vectors with positive integral coordinates is investigated. It is proved that each such semigroup contains a sub-semigroup isomorphic to a convex hull (in the lattice) of this semigroup.Translated from Ukrainskii Geometricheskii Sbornik, No. 35, pp. 99–103, 1992. 相似文献
20.
I. A. Dynnikov 《Functional Analysis and Its Applications》2000,34(1):24-32
An explicit construction of a finitely presented semigroup whose central elements are in a one-to-one correspondence with
the isotopy classes of unoriented links in the three-space is given, together with a finite presentation for the group of
invertible elements of the semigroup. The group is presented by two generators and three relations. The commutator subgroup
of the group is isomorphic to the braid group of infinite index. A similar construction is given for band-links. The kauffman
theorems on the existence of polynomial band-link invariants satisfying some skein-relations are stated algebraically.
This work is partially supported by Russian Foundation for Basic Research grant No. 99-01-00090.
Moscow State University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 34, No. 1, pp. 29–40, January–March,
2000.
Translated by I. a. Dynnikov 相似文献