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The Probability That an Element of a Group Fixes a Set and the Group Act on Set by Conjugation

S. M. S. Omer, N. H. Sarmin, A. Erfanian, K. Moradipour


The commutativity degree is the probability that two random elements commute in G, and denoted as P(G). The main purposes of this paper is to find the probability of an element of a group G fixes a set X. The set X is in the form (a; b), where a and b are commuting element in G of size 2 and the group G acts on the set of all subset of X by conjugation. A new definition of this probability is introduced. Among other results, some upper bounds for P(G) are provided.


Commutativity degree, group action, conjugation.

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