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1.
Atournament regular representation (TRR) of an abstract groupG is a tournamentT whose automorphism group is isomorphic toG and is a regular permutation group on the vertices ofT. L. Babai and W. Imrich have shown that every finite group of odd order exceptZ
3 ×Z
3 admits a TRR. In the present paper we give several sufficient conditions for an infinite groupG with no element of order 2 to admit a TRR. Among these are the following: (1)G is a cyclic extension byZ of a finitely generated group; (2)G is a cyclic extension byZ
2n+1 of any group admitting a TRR; (3)G is a finitely generated abelian group; (4)G is a countably generated abelian group whose torsion subgroup is finite. 相似文献
2.
For a finite group G, let E(G) denote the near-ring of functions generated by the semigroup, End(G), of endomorphisms of G. We characterize when E(G) is maximal as a subnear-ring of M
0(G). A group G is an E-group if E(G) is a ring. We give a new characterization of finite E-groups and investigate the problem of determining, for finite E-groups, when E(G) is maximal as a ring in M0(G).
Received: 26 June 2006 相似文献
3.
We prove that a finitely generated group G is virtually free if and only if there exists a generating set for G and k > 0 such that all k-locally geodesic words with respect to that generating set are geodesic.
Received: 30 October 2006 相似文献
4.
Let R(G) denote the intersection of all nonnormal subgroups of a group G. In this note, we prove that for every finite group G, if R(G) is not trivial, then the normalizer property holds forG. 相似文献
5.
Martin R. Pettet 《Archiv der Mathematik》2006,86(1):26-30
If an infinite group G admits a free action by a group of automorphisms A which is virtually an FC-group and which has only finitely many orbits,
then G is isomorphic to the additive group of a field and the action is that of a group of semilinear transformations.
Received: 21 February 2005 相似文献
6.
Marius Tărnăuceanu 《Quaestiones Mathematicae》2019,42(1):87-92
In this note we give some new results concerning the subgroup commutativity degree of a finite group G. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of G. 相似文献
7.
George M. Bergman 《Algebra Universalis》1989,26(3):267-283
For the standard operators on classes of algebras,H (homomorphic images),S (subalgebras) andP (products), and the further operatorP
f
of finite products, it is shown by counterexamples thatHSP SHPS andHSP
f
SHP
fS for metabelian groups (groups satisfyingG={e}) and thatHSP
f
SHPS for solvable groups (in fact, for finite groups satisfying (G, G)= {e}). From the first two inequalities and some easier examples, it follows that the partially ordered semigroups of operators on metabelian groups generated by {H, S, P} and by {H, S, P
f
} are as in the standard 18-element diagram.In Memory of Evelyn NelsonThis work was done while the author was partly supported by NSF contracts MCS 82-02632 and DMS 85-02330.Presented by Robert W. Quackenbush. 相似文献
8.
The shift action on the 2-cocycle group Z2(G,C) of a finite group G with coefficients in a finitely generated abelian group C has several useful applications in combinatorics and digital communications, arising from the invariance of a uniform distribution property of cocycles under the action. In this article, we study the shift orbit structure of the coboundary subgroup B2(G,C) of Z2(G,C). The study is placed within a well-known setting involving the Loewy and socle series of a group algebra over G. We prove new bounds on the dimensions of terms in such series. Asymptotic results on the size of shift orbits are also derived; for example, if C is an elementary abelian p-group, then almost all shift orbits in B2(G,C) are maximal-sized for large enough finite p-groups G of certain classes. 相似文献
9.
In this note, we show that if
is a π-partial character of the π-separable group
is a chain of normal subgroups of G, and H is a Hall π-subgroup of G, then
has a Fong character α
Irr(H) such that for every subgroup
, every irreducible constituent of α
H∩N
is Fong for N. We also show that if
is quasi-primitive, then for every normal subgroup M of G the irreducible constituents of
are Fong for M.
Received: 21 July 2006 Revised: 17 January 2007 相似文献
10.
M. C. Crabb 《Journal of Fixed Point Theory and Applications》2007,2(2):171-193
We describe an equivariant version (for actions of a finite group G) of Dold’s index theory, [10], for iterated maps. Equivariant Dold indices are defined, in general, for a G-map U → X defined on an open G-subset of a G-ANR X (and satisfying a suitable compactness condition). A local index for isolated fixed-points is introduced, and the theorem
of Shub and Sullivan on the vanishing of all but finitely many Dold indices for a continuously differentiable map is extended
to the equivariant case. Homotopy Dold indices, arising from the equivariant Reidemeister trace, are also considered.
相似文献
11.
Let Kbe a field of characteristic p> 0. Denote by ω(R) the augmentation ideal of either a group algebra (R) = K[G] or a restricted enveloping algebra R= u(L) over K. We first characterize those Rfor which ω(R) satisfies a polynomial identity not satisfied by the algebra of all 2 × 2 matrices over K. Then, we examine those Rfor which U J(R) satisfies a semigroup identity (that is, a polynomial identity which can be written as the difference of two monomials). 相似文献
12.
Otmar Venjakob 《Journal of the European Mathematical Society》2002,4(3):271-311
This paper is motivated by the question whether there is a nice structure theory of finitely generated modules over the Iwasawa
algebra, i.e. the completed group algebra, Λ of a p-adic analytic group G. For G without any p-torsion element we prove that Λ is an Auslander regular ring. This result enables us to give a good definition of the notion
of a pseudo-nullΛ-module. This is classical when G=ℤ
k
p
for some integer k≥1, but was previously unknown in the non-commutative case. Then the category of Λ-modules up to pseudo-isomorphisms is studied
and we obtain a weak structure theorem for the ℤ
p
-torsion part of a finitely generated Λ-module. We also prove a local duality theorem and a version of Auslander-Buchsbaum
equality. The arithmetic applications to the Iwasawa theory of abelian varieties are published elsewhere.
Received May 12, 2001 / final version received July 5, 2001?Published online September 3, 2001 相似文献
13.
For a large class of groups G a precise congruence subgroup of the group generated by the bicyclic units of the integral group ring ZG is determined. As an application an upper bound is calculated for the index in the unit group of ZG for the group generated by the Bass cyclic units and the bicyclic units. 相似文献
14.
Let KG be a group algebra of a finite p-group G over a finite field Kof characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group with a cyclic group of order 4 or G has an abelian subgroup A of index 2 and an element b such that b inverts each element of A. 相似文献
15.
Let p be a prime, G
a finite group which has a normal p-subgroup
containing its own centralizer in G, and
R a commutative local ring with residue class
field of characteristic p. In this paper, it is
shown that if
is an augmented automorphism of
RG which fixes a Sylow
p-subgroup P
of G, there is
such that
for all
and
is an inner automorphism of
RG.
Received: 26 July 2000 相似文献
16.
B. A. F. Wehrfritz 《Monatshefte für Mathematik》2000,129(2):153-157
Let V be a left vector space over a division ring D and the group of all D-automorphisms of V. A subgroup G of is completely reducible of V is completely reducible as D–G bimodule. Our aim in this brief note is to point out that in a sense the very useful notion of a local marker extends from
V finite-dimensional to V infinite-dimensional. (A local marker of a subgroup G of is any finitely generated subgroup X of G such that row n-space has least composition length as D–X bimodule. A local marker of G controls to a considerable extent the local behaviour of G.)
Our main result is the following. Let G be a completely reducible subgroup of and let W be any finite-dimensional D-subspace of V. Then G has a finitely generated subgroup X such that for every finitely generated subgroup Y of G containing X the D–Y submodule WY has a D–Y submodule M with and completely reducible. We also give some examples and state without proof some stronger conclusions valid for various special
subgroup G.
(Received 21 December 1998; in revised form 31 May 1999) 相似文献
17.
Jeremy Haefner 《代数通讯》2013,41(2):445-481
We give necessary conditions for a map to be irreducible (in the category of finitely generated, torsion free modules) over a non-local, commutative ring and sufficient conditions when the ring is Bass. In particular, we show that an irreducible map of ZG, where G is a square free abelian group, must be a monomorphism with a simple cokernel. We also show that local endomorphism rings are necessary and sufficient for the existence of almost split sequences over a commutative Bass ring and we explicitly describe the modules and the maps in those sequences. The results in this paper enable us to describe the Auslander-Reiten quiver of a non-local Bass ring in [8]. 相似文献
18.
Nathan S. Feldman 《Integral Equations and Operator Theory》2007,58(2):153-173
A pair of commuting operators, (A,B), on a Hilbert space
is said to be hypercyclic if there exists a vector
such that {A
n
B
k
x : n, k ≥ 0} is dense in
. If f, g ∈H
∞(G) where G is an open set with finitely many components in the complex plane, then we show that the pair (M
*
f
, M
*
g
) of adjoints of multiplcation operators on a Hilbert space of analytic functions on G is hypercyclic if and only if the semigroup they generate contains a hypercyclic operator. However, if G has infinitely many components, then we show that there exists f, g ∈H
∞(G) such that the pair (M
*
f
, M
*
g
) is hypercyclic but the semigroup they generate does not contain a hypercyclic operator. We also consider hypercyclic n-tuples. 相似文献
19.
For a Hall system of a finite solvable group G, it is known that the set
of -permutable subgroups is a sublattice of the subgroup lattice of G. We investigate the class SPM of groups in which the lattice
is modular. We prove that if
is modular, then U V for all
(an evidently stronger condition). Both of these phenomena—the modularity of
and whether two -permutable subgroups U and V permute with each other—are shown to be determined locally, by what happens at each prime. The class SPM is shown to be quotient closed, but not direct product or subgroup closed.This revised electronic version of the Abstract includes the formulas that were missing in the previous electronic version published online in September 2004. 相似文献
20.
In this paper we consider certain subalgebras of the Green algebra (representation algebra) of a finite group G. One such algebra is spanned by the isomorphism classes of all indecomposable modules whose source is an endo-permutation module. This algebra can be embedded into a finite direct product of Laurent polynomial rings in finitely many variables over a field. Another such algebra is spanned by the isomorphism classes of all irreducibly generated modules. When G is p-solvable then this algebra is finite-dimensional and split semisimple.R. Boltje was supported by the NSF, DMS-0200592 and 0128969. B. Külshammer was supported by the DAAD. 相似文献