## “School of Mathematics”

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Paper   IPM / M / 16717
School of Mathematics
Title:   Commuting probability of compact groups
Author(s):
 1 Alireza Abdollahi 2 Meisam Soleimani Malekan
Status:   Published
Journal: Bull. Aust. Math. Soc.
Year:  2021
Pages:   DOI: 10.1017/S0004972721000472
Supported by:  IPM
Abstract:
For any (Hausdorff) compact group G, denote by cp(G) the probability that a randomly chosen pair of elements of G commute. We prove that there exists a finite group H such that cp(G) = cp(H)/ - G : F - 2, where F is the FC-centre of G and H is isoclinic to F with cp(F) = cp(H) whenever cp(G) > 0. In addition, we prove that a compact group G with cp(G) > 40 3 is either solvable or isomorphic to A5 Ã Z(G), where A5 denotes the alternating group of degree five and the centre Z(G) of G contains the identity component of G.