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

Full content URL: http://www.theoryofgroups.ir/article_761_59.html

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Item Type: | Article |
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Item Status: | Live Archive |

## 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 |
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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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