On the Number of Conjugacy Classes of -elements in Finite Groups
نویسندگان
چکیده
Let G be a nite group and be a set of primes. Put d (G) = k (G)=jGj where k (G) is the number of conjugacy classes of -elements in G and jGj is the -part of the order of G. In this paper we initiate the study of this invariant by showing that if d (G) > 5=8 then G possesses an abelian Hall -subgroup, all Hall -subgroups of G are conjugate, and every -subgroup of G lies in some Hall -subgroup of G. Furthermore we have d (G) = 1 or d (G) = 2=3. This extends and generalizes a result of W. H. Gustafson.
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