On p-soluble groups with a generalized p-central or powerful sylow p-subgroup

Khukhro, Evgeny (2012) On p-soluble groups with a generalized p-central or powerful sylow p-subgroup. International Journal of Group Theory, 1 (2). pp. 51-57. ISSN 2251-7650

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Abstract

Let G be a finite p-soluble group, and P a Sylow p-subgroup of G. It is proved that if all elements of P of order p (or of order ≤ 4 for p = 2) are contained in the k-th term of the upper central series of P, then the p-length of G is at most 2m+1, where m is the greatest integer such that pm - pm-1 ≤ k, and the exponent of the image of P in G/Op′,p(G) is at most pm. It is also proved that if P is a powerful p-group, then the p-length of G is equal to 1. 2012 University of Isfahan.

Keywords:p-central p-group of height k, powerful p-group, p-soluble, p-length
Divisions:College of Science > School of Mathematics and Physics
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ID Code:15584
Deposited On:28 Oct 2014 11:50

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