Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups

Details Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups Relative n-isoclinism classes and relative n-th nilpotency degree of finite groups

2010-03-11

arxiv.org/abs/1003.2306v1

Mathematics

Group Theory

11 pages, series of contributions on the topic of the same authors

Scientific paper

The purpose of the present paper is to consider the notion of isoclinism between two finite groups and its generalization to n-isoclinism, introduced by J. C. Bioch in 1976. A weaker form of n-isoclinism, called relative n-isoclinism, will be discussed. This will allow us to improve some classical results in literature. We will point out the connections between a relative n-isoclinism and the notions of commutativity degree, n-th nilpotency degree and relative n-th nilpotency degree, which arouse interest in the classification of groups of prime power order in the last years.

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