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| Paper IPM / M / 16717 |
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| Abstract: | |||||
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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.
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