Nonabelian sylow subgroups of finite groups of even order, in preparation.

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Author	Iiyori, Nobuo Chigira, Naoki Yamaki, Hiroyoshi
Abstract	Abstract. We have been able to prove that every nonabelian Sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution. The proof depends upon the consequences of the classifi-cation of finite simple groups. The purpose of this note is to announce [4]: Main Theorem. Every nonabelian Sylow subgroup of a finite group of even order contains a nontrivial element which commutes with an involution. Let G be a nite group and Γ(G) the prime graph of G. Γ(G) is the graph such that the vertex set is the set of prime divisors of jGj, and two distinct vertices p and r are joined by an edge if and only if there exists an element of order pr in G. Let n(Γ(G)) be the number of connected components of Γ(G) and dG(p, r) the distance between two vertices p and r of Γ(G). It has been proved that n(Γ(G)) 6 in [12], [10], [11], [9]. Theorem 1. Let G be a finite group of even order and p a prime divisor of jGj. If dG(2, p) 2, then a Sylow p-subgroup of G is abelian.
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