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

Abstract

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.

11 pages, to appear in Filomat with revisions

References in corpus (1)

• A generalization of the probability that the commutator of two group elements is equal to a given element

Cited by in corpus (5)

• Commuting powers and exterior degree of finite groups
• A generalization of the probability that the commutator of two group elements is equal to a given element
• Remarks on the tensor degree of finite groups
• Considerations on the subgroup commutativity degree and related notions
• Subgroup S-commutativity degrees of finite groups