On the degree of commutativity of  p  ‐groups of maximal class | Zendy

Vera–López A. | Zendy; Arregi J.M. | Zendy; Jaikin–Zapirain A. | Zendy

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

Author(s) -

Vera–López A.,

Arregi J.M.,

Jaikin–Zapirain A.

Publication year - 2008

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200510703

Subject(s) - mathematics , modulo , commutative property , degree (music) , class (philosophy) , order (exchange) , combinatorics , lie group , lie algebra , pure mathematics , discrete mathematics , physics , finance , artificial intelligence , computer science , acoustics , economics

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: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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