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On -groups of maximal class

✍ Scribed by A. Jaikin-Zapirain; A. Vera-López

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
237 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Finite groups, maximal class MSC (2010) 20D15

Let R be the ring Z[x]/ x p -1

x -1 = Z[x] and let a be the ideal of R generated by (x -1). In this paper, we discuss the structure of the Z[Cp ]-module (R/a n -1 )∧(R/a n -1 ), which plays an important role in the theory of p-groups of maximal class (see [2]-[5]). The generators of this module allow us to obtain the defining relations of some important examples of p-groups of maximal class with Y1 of class two. In particular we obtain the best possible estimates for the degree of commutativity of p-groups of maximal class with Y1 of class two.

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