§ 217. Nonabelian p-groups all of whose elements contained in any minimal nonabelian subgroup are of breadth < 2

2016 ◽  
Keyword(s):  
Nonabelian Subgroup

scholarly journals Derangements in cosets of primitive permutation groups

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Andrei Pavelescu
Keyword(s):  
Fixed Point ◽  
Finite Fields ◽  
Permutation Groups ◽  
Normal Subgroups ◽  
Primitive Groups ◽  
Branched Coverings ◽  
Affine Groups ◽  
Nonabelian Subgroup ◽  
Projective Curves ◽  
Curves Over Finite Fields

AbstractMotivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups. Using the Aschbacher–O'Nan–Scott Theorem for primitive groups to partition the problem, we provide complete answers for affine groups and groups which contain a regular normal nonabelian subgroup.

Finite groups all of whose small subgroups are normal

2014 ◽  
Vol 13 (06) ◽  
pp. 1450006 ◽  
Author(s):  
Yakov Berkovich
Keyword(s):  
Finite Groups ◽  
Crucial Role ◽  
Maximal Order ◽  
Nonabelian Subgroup ◽  
Abelian Subgroups

The finite groups G such that, whenever H < G and |H|2 < |G|, then H ◃ G are classified in Theorems 2.1 and 3.2. Let pν(X)(pa(X)) be the maximal order of an abelian (a minimal nonabelian) subgroup of a p-group X. We classify the p-groups G such that, whenever an abelian H < G and |H| ≤ pν(G)-2, then H ◃ G. Next, we describe the p-groups G all of whose abelian subgroups of order ≤ pa(G)-2 are normal. Minimal nonabelian and minimal nonnilpotent groups play crucial role in the whole paper.

FINITE GROUPS IN WHICH ALL NONABELIAN SUBGROUPS ARE TI-SUBGROUPS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350074 ◽  
Author(s):  
JIANGTAO SHI ◽  
CUI ZHANG
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Nonabelian Subgroup ◽  
A Finite Group

In this paper, we show that G is a finite group in which every nonabelian subgroup is a TI-subgroup if and only if every nonabelian subgroup of G is normal in G.

scholarly journals FINITE INDEX SUBGROUPS OF FULLY RESIDUALLY FREE GROUPS

2011 ◽  
Vol 21 (04) ◽  
pp. 651-673 ◽  
Author(s):  
ANDREY V. NIKOLAEV ◽  
DENIS E. SERBIN
Keyword(s):  
Free Group ◽  
Finite Index ◽  
Free Groups ◽  
Graph Theoretic ◽  
Nonabelian Subgroup ◽  
Finite Index Subgroups

Using graph-theoretic techniques for f.g. subgroups of Fℤ[t] we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. As an application we obtain an analogue of Greenberg–Stallings Theorem for f.g. fully residually free groups, and prove that a f.g. nonabelian subgroup of a f.g. fully residually free group is of finite index in its normalizer and commensurator.

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