Topic
Regular p-group
About: Regular p-group is a research topic. Over the lifetime, 5 publications have been published within this topic receiving 21 citations.
Papers
TL;DR: It is proved that if GR is not normal in Aut(X) then X≅[2K1] with n>1, Aut( X) ≅Z2wrZ2n, and either G=Z2 n+1= and S={a,a2n+1}, or G= Z2n×Z2=× and S=a,ab.
Abstract: Let X=Cay(G,S) be a 2-valent connected Cayley digraph of a regular p-group G and let G R be the right regular representation of G. It is proved that if G R is not normal in Aut(X) then X≅\(\)[2K 1 ] with n>1, Aut(X) ≅Z 2 wrZ 2n , and either G=Z 2n+1 = and S={a,a 2n+1 }, or G=Z 2n ×Z 2 = × and S={a,ab}.
11 citations
TL;DR: In this paper, the order of a non-Dedekind C(pw)-group cannot exceed p4w+4 when p > 2 and G′ ≤ HG for every non-normal cyclic subgroup H.
Abstract: A p-group is called a C(pw)-group if the normal closure of every non-normal cyclic subgroup has index at most pw. In this paper, we prove that the order of a non-Dedekind C(pw)-group cannot exceed p4w+4 when p > 2 and G′ ≤ HG for every non-normal cyclic subgroup H. We also completely classify non-Dedekind C(p2)-groups for p > 2.
5 citations
Posted Content•
TL;DR: In this article, a sharp bound for the nilpotency class of a regular p-group in terms of its coexponent is derived, which is used to show that the number of groups of order p^n with a given fixed co-exponent, is independent of n, for p and n sufficiently large.
Abstract: A sharp bound is derived for the nilpotency class of a regular p-group in terms of its coexponent, and is used to show that the number of groups of order p^n with a given fixed coexponent, is independent of n, for p and n sufficiently large. Explicit formulae are calculated in the case of coexponent 3.
4 citations
TL;DR: In this paper, a sharp bound for the nilpotency class of a regular p-group in terms of its coexponent is derived, which is used to show that the number of groups of order pn with a given fixed co-exponent, is independent of n, for p and n sufficiently large.
Abstract: A sharp bound is derived for the nilpotency class of a regular p-group in terms of its coexponent, and is used to show that the number of groups of order pn with a given fixed coexponent, is independent of n, for p and n sufficiently large. Explicit formulae are calculated in the case of coexponent 3.
3 citations
TL;DR: In this paper, it was shown that a Sylow p-subgroup of the general linear group of dimension n over the residue ring modulo pm is regular for n 2 < p and powerful if and only if n = 2 and m = 1.
Abstract: We prove that a Sylow p-subgroup of the general linear group of dimension n over the residue ring modulo pm is regular for n2 < p and powerful if and only if n = 2 and m = 1. We obtain similar results for the Sylow p-subgroups of normal types over the same ring.
1 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2014 | 1 |
| 2006 | 1 |
| 2002 | 1 |
| 2000 | 1 |
| 1998 | 1 |