Multiplicities in Sylow Sequences and the Solvable Radical
نویسندگان
چکیده
A complete Sylow sequence, P = P1, . . . , Pm , of a finite group G is a sequence of m Sylow pi -subgroups of G, one for each pi , where p1, . . . , pm are all of the distinct prime divisors of |G|. A product of the form P1 · · · Pm is called a complete Sylow product of G. We prove that the solvable radical of G equals the intersection of all complete Sylow products of G if, for every composition factor S of G, and for every ordering of the prime divisors of |S|, there exist a complete Sylow sequence P of S, and g ∈ S such that g is uniquely factorizable in P . This generalizes our results in Kaplan and Levy [‘The solvable radical of Sylow factorizable groups’, Arch. Math. 85(6) (2005), 490–496]. 2000 Mathematics subject classification: 20D25.
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