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The exact bounds for the degree of commutativity of a p-group of maximal class, I

✍ Scribed by Antonio Vera-López; J.M. Arregi; M.A. Garcı́a-Sánchez; F.J. Vera-López; R. Esteban-Romero

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
209 KB
Volume
256
Category
Article
ISSN
0021-8693

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✦ Synopsis

The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the 'degree of commutativity.' Recently (1995) Fernández-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-López et al., preprint]. In this paper, we prove two of these conjectures.

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On the degree of commutativity of p -gro
On the degree of commutativity of p -groups of maximal class
✍ A. Vera–López; J.M. Arregi; A. Jaikin–Zapirain 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 161 KB

## 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