On the degree of commutativity of p ‐groups of maximal class |
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| Authors: | A Vera–López JM Arregi A Jaikin–Zapirain |
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| Institution: | 1. Departamento de Matemáticas, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain;2. Phone: +34 946012647, Fax: +34 946012516;3. Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, Cantoblanco Ciudad Universitaria, 28049 Madrid, Spain;4. Phone: +34 914974940, Fax: +34 914974889 |
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| Abstract: | Let G be a p ‐group of maximal class of order pm , p ≠ 2, and c (G) the degree of commutativity of G. Let c0 be the nonnegative residue of c modulo p – 1. In this paper, by using only Lie algebra techniques, we prove that 2c ≥ m – 2p + c 0 + 1. Also, we give examples of Lie algebras satisfying the following equalities: ![equation image]( "equation image") In addition, there exist examples of p ‐groups of maximal class satisfying 2c = m – 2p + c0 + 3 for each c0 ∈ 2, p – 2] (see 6, Theorem 4.5]). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Finite groups maximal class |
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