关于有限群的正规π-补的存在性

主要证明了如下二结果 :(1)假设 3 π并且有限群G的每个非Abel单截段之阶的形如 4n - 1的素因数的个数是偶数 ,则G是π′ 闭的当且仅当G是π 齐次的 ;(2 )假设对于有限群G的任一单截段A B ,|A B|之形如 4n - 1的素因数的个数是偶数并且只要A B PSL(2 ,p) ,p是一个形如 4n 1的素数使得n(2n 1) 0 (mod 5 ) ,那么G是π′ 闭的当且仅当G是π 齐次的 .

On the Existence of Normal π-Complements in Finite Groups

In this note, the following two results are proved.(1) Suppose that 3()π and the number of prime divisors of type 4n-1 of the order of each each nonabelian simple section of a finite group G is even. Then G is π′-closed if and only if G is π-homogenous. (2) Suppose that for any simple section A/B of a finite group G the number of prime divisors of type 4n-1 in |A/B| is even and whenever A/B(≌)PSL(2,p), p is not a prime of type 4n+1 such that n(2n+1)(≠)0(mod 5). Then G is π′-closed if and only if G is π-homogenous.