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On the degree of commutativity of p -groups of maximal class

✍ Scribed by A. Vera–López; J.M. Arregi; A. Jaikin–Zapirain

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
161 KB
Volume
281
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let G be a p ‐group of maximal class of order p^m^ , p ≠ 2, and c (G) the degree of commutativity of G. Let c~0~ be the nonnegative residue of c modulo p – 1. In this paper, by using only Lie algebra techniques, we prove that 2__c ≥ m__ – 2__p__ + c 0 + 1. Also, we give examples of Lie algebras satisfying the following equalities:

equation image

In addition, there exist examples of p ‐groups of maximal class satisfying 2__c__ = m – 2__p__ + c~0~ + 3 for each c~0~ ∈ [2, p – 2] (see [6, Theorem 4.5]). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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