A descent principle in modular subgroup arithmetic

Peter J. Cameron*, Thomas W. Müller

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We establish and comment on a surprising relationship between the behaviour modulo a prime p of the number sn (G) of index n subgroups in a group G, and that of the corresponding subgroup numbers for a subnormal subgroup of p-power index in G. One of the applications of this result presented here concerns the explicit determination modulo p of sn (G) in the case when G is the fundamental group of a finite graph of finite p-groups. As another application, we extend one of the main results of the second author's paper (Forum Math, in press) concerning the p-patterns of free powers G* q of a finite group G with q a p-power to groups of the more general form H* G*q, where H is any finite p-group.

Original languageEnglish
Pages (from-to)189-203
Number of pages15
JournalJournal of Pure and Applied Algebra
Volume203
Issue number1-3
DOIs
Publication statusPublished - 1 Dec 2005

Fingerprint

Dive into the research topics of 'A descent principle in modular subgroup arithmetic'. Together they form a unique fingerprint.

Cite this