The structure of finite groups with three class sizes
نویسندگان
چکیده
Let G be a finite group and suppose that the set of conjugacy class sizes of G is f1;m;mng, where m; n > 1 are coprime. We prove that m 1⁄4 p for some prime p dividing n 1. We also show that G has an abelian normal p-complement and that if P is a Sylow p-subgroup of G, then jP 0j 1⁄4 p and jP=ZðGÞpj 1⁄4 p. We obtain other properties and determine completely the structure of G.
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