78 research outputs found
On self-normalising subgroups of finite groups
The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively
Compression of Finite Group Actions and Covariant Dimension, II
Let be a finite group and an equivariant morphism of
finite dimensional -modules. We say that is faithful if acts
faithfully on . The covariant dimension of is the minimum of the
dimension of taken over all faithful . In \cite{KS07} we
investigated covariant dimension and were able to determine it in many cases.
Our techniques largely depended upon finding homogeneous faithful covariants.
After publication of \cite{KS07}, the junior author of this article pointed out
several gaps in our proofs. Fortunately, this inspired us to find better
techniques, involving multihomogeneous covariants, which have enabled us to
extend and complete the results, simplify the proofs and fill the gaps of
\cite{KS07}
On a class of p-soluble groups
Electronic version of an article published as Algebra Colloquium, 12(2)(2005), 263-267 DOI: 10.1142/S1005386705000258. © copyright World Scientific Publishing Company. http://www.worldscientific.com/doi/abs/10.1142/S1005386705000258[EN] Let p be a prime. The class of all p-soluble groups G such that every p-chief factor of G is cyclic and all p-chief factors of G are G-isomorphic is studied in this paper. Some results on T-, PT-, and
PST -groups are also obtained.Supported by Grant BFM2001-1667-C03-03, MCyT (Spain) and FEDER (European Union)http://www.worldscientific.com/doi/abs/10.1142/S1005386705000258Ballester Bolinches, A.; Esteban Romero, R.; Pedraza Aguilera, MC. (2005). On a class of p-soluble groups. Algebra Colloquium. 2(12). doi:10.1142/S100538670500025821
On finite groups with many supersoluble subgroups
The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2(5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2(5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201-206, 2012)
Generators and commutators in finite groups; abstract quotients of compact groups
Let N be a normal subgroup of a finite group G. We prove that under certain
(unavoidable) conditions the subgroup [N,G] is a product of commutators [N,y]
(with prescribed values of y from a given set Y) of length bounded by a
function of d(G) and |Y| only. This has several applications: 1. A new proof
that G^n is closed (and hence open) in any finitely generated profinite group
G. 2. A finitely generated abstract quotient of a compact Hausdorff group must
be finite. 3. Let G be a topologically finitely generated compact Hausdorff
group. Then G has a countably infinite abstract quotient if and only if G has
an infinite virtually abelian continuous quotient.Comment: This paper supersedes the preprint arXiv:0901.0244v2 by the first
author and answers the questions raised there. Latest version corrects
erroneous Lemma 4.30 and adds new Cor. 1.1
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