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Paper   IPM / M / 16717
School of Mathematics
  Title:   Commuting probability of compact groups
1.  Alireza Abdollahi
2.  Meisam Soleimani Malekan
  Status:   Published
  Journal: Bull. Aust. Math. Soc.
  Year:  2021
  Pages:   DOI: 10.1017/S0004972721000472
  Supported by:  IPM
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 × Z(G), where A5 denotes the alternating group of degree five and the centre Z(G) of G contains the identity component of G.

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