2~a3~bp^cq^d(p≡1(mod q))阶单群

运用单群分类定理 ,给出了阶为 2 a3bpcqd(p≡ 1(mod q) )的所有K4 - 单群 ,从而 ,给出了 p≡ 1(modq) (p是 |G|的最大素因子 ,q是 |G|的次大素因子 )的所有K4 -

Simple groups with orders 2~a3~b5~cp^d, 2~a3~b7~cp^d and 2~a3~b5~c7~d

This work deals with the power exponent 1rand 2r respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple 4{5,7}K--group G (i.e. G can not be divided by 5 nor by 7 or ()Gp= 4 ), simple 5 -4K-group G (i.e. G can not divided by 5 and ()Gp=4) and simple 7-4K-group G (i.e. G can not divided by 7 and ()Gp= 4). It is derived that 1r =1, 2 and 4, and 2r is not greater than 4. All the simple 4K-groups with order 235,237abcdabcdpp and 2357abcd are obtained.