共查询到20条相似文献,搜索用时 343 毫秒
1.
It is known that if a group contains an abelian subgroup of finite index, then it also has an abelian characteristic subgroup of finite index. The aim of this paper is to prove that corresponding results hold when abelian subgroups are replaced either by subgroups having a modular subgroup lattice or by quasihamiltonian subgroups. 相似文献
2.
Ivan Arzhantsev 《代数通讯》2018,46(8):3539-3552
A non-degenerate toric variety X is called S-homogeneous if the subgroup of the automorphism group Aut(X) generated by root subgroups acts on X transitively. We prove that maximal S-homogeneous toric varieties are in bijection with pairs (P,𝒜), where P is an abelian group and 𝒜 is a finite collection of elements in P such that 𝒜 generates the group P and for every a∈𝒜 the element a is contained in the semigroup generated by 𝒜?{a}. We show that any non-degenerate homogeneous toric variety is a big open toric subset of a maximal S-homogeneous toric variety. In particular, every homogeneous toric variety is quasiprojective. We conjecture that any non-degenerate homogeneous toric variety is S-homogeneous. 相似文献
3.
Igor Dolinka 《Periodica Mathematica Hungarica》2012,65(1):97-105
We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands. 相似文献
4.
5.
The maximal ideal space ΔG of the measure algebra M(G) of a locally compact abelian group G is a compact commutative semitopological semigroup. In this
paper we show that cℓ Ĝ the closure of Ĝ, the dual of G, in ΔG can contain maximal subgroups which are not locally compact. We have previously characterized the locally compact maximal
subgroups of cℓ Ĝ as arising from locally compact topologies on G which are finer than the original topology.
This research was supported in part by NSF contract number GP-19852. 相似文献
6.
7.
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister-Schreier type rewriting. 相似文献
8.
A semigroup is complex if it generates a variety the subvariety lattice of which contains an isomorphic copy of every finite
lattice. It is known that a complex semigroup has at least four elements and that up to isomorphism and anti-isomorphism,
there are four complex semigroups of order four. Subvarieties of the varieties generated by two of these four minimal complex
semigroups have previously been described. To complete the study, we describe subvarieties of the varieties generated by the
remaining two semigroups.
This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science
Foundation of Gansu Province (No.3ZS052-A25-017) 相似文献
9.
In [6] it is shown that the maximal subgroups of the free idempotent generated regular semigroup which is determined by the
biordered set of a completely O-simple semigroup are free. In this note we shall extend this result to a wider class of semigroups. 相似文献
10.
The combinatorial simple principal ideal semigroups generated by two elements were described by L. Megyesi and G. Pollák.
The ‘most general’ among them is called the Rédei semigroup. The ‘most special’ combinatorial simple principal ideal semigroup
generated by two elements is the bicyclic semigroup. D. B. McAlister determined the compatible semilattice orders on the bicyclic
semigroup. Our aim is to study the compatible semilattice orders on the homomorphic images of the Rédei semigroup. We prove
that there are four compatible total orders on these semigroups. We show that on the Rédei semigroup, the total orders are
the only compatible semilattice orders. Moreover, on each proper homomorphic image of the Rédei semigroup, we give a compatible
semilattice order which is not a total order.
Communicated by Mária B. Szendrei 相似文献
11.
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13.
thNNTWA New Characterization of Simple K_3-groups@王临红&& 相似文献
14.
B.M. Vernikov 《Semigroup Forum》2007,75(3):554-566
We call a semigroup variety modular [upper-modular, lower-modular, neutral] if it is a modular [respectively upper-modular,
lower-modular, neutral] element of the lattice of all semigroup varieties. It is proved that if V is a lower-modular variety
then either V coincides with the variety of all semigroups or V is periodic and the greatest nil-subvariety of V may be given
by 0-reduced identities only. We completely determine all commutative lower-modular varieties. In particular, it turns out
that a commutative variety is lower-modular if and only if it is neutral. A number of
corollaries of these results are obtained. 相似文献
15.
Benjamin Steinberg 《Semigroup Forum》2010,81(1):217-227
We associate a 2-complex to the following data: a presentation of a semigroup S and a transitive action of S on a set V by partial transformations. The automorphism group of the action acts properly discontinuously on this 2-complex. A sufficient
condition is given for the 2-complex to be simply connected. As a consequence we obtain simple topological proofs of results
on presentations of Schützenberger groups. We also give a geometric proof that a finitely generated regular semigroup with
finitely many idempotents has polynomial growth if and only if all its maximal subgroups are virtually nilpotent. 相似文献
16.
It is shown that the isomorphy classes of the ideals of a valuation domain form a Clifford semigroup, and the structure of
this semigroup is investigated. The group constituents of this Clifford semigroup are exactly the quotients of totally ordered
complete abelian groups, modulo dense subgroups. A characterization of these groups is obtained, and some realization results
are proved when the skeleton of the totally ordered group is given.
The authors are members of GNSAGA of CNR. This research was supported by Ministero dell'Università e della Ricerca Scientifica
e Tecnologica, Italy. 相似文献
17.
Norman R. Reilly 《Semigroup Forum》2012,84(1):176-199
In a manner similar to the construction of the fundamental group of a connected graph, this article introduces the construction
of a fundamental semigroup associated with a bipartite graph. This semigroup is a 0-direct union of idempotent generated completely
0-simple semigroups. The maximal nonzero subgroups are the corresponding fundamental groups of the connected components. Adding
labelled edges to the graph leads to a more general completely 0-simple semigroup. The basic properties of such semigroups
are examined and they are shown to have certain universal properties as illustrated by the fact that the free completely simple
semigroup on n generators and its idempotent generated subsemigroup appear as special cases. 相似文献
18.
We study the maximal subgroups of free idempotent generated semigroups on a biordered set by topological methods. These subgroups are realized as the fundamental groups of a number of 2-complexes naturally associated to the biorder structure of the set of idempotents. We use this to construct the first example of a free idempotent generated semigroup containing a non-free subgroup. 相似文献
19.
Avino’am Mann 《Israel Journal of Mathematics》1968,6(1):13-25
A group is said to have dense normal subgroups, if each non-empty open interval in its lattice of subgroups contains a normal
subgroup. The structure of this and related classes of groups is investigated. Typical results are: an infinite group with
dense ascendant subgroups is locally nilpotent: a nontorsion group with dense normal subgroups is abelian, etc. 相似文献
20.
B. M. Vernikov 《Journal of Mathematical Sciences》2010,164(2):182-187
A semigroup variety is called a variety of degree ≤2 if all its nilsemigroups are semigroups with zero multiplication, and a variety of degree >2 otherwise. We completely determine all semigroup varieties of degree >2 that are upper-modular elements of the lattice of all semigroup varieties and find quite a strong necessary condition for
semigroup varieties of degree ≤2 to have the same property. 相似文献