交错群A_5,A_6,A_7的新刻画

New Characterization of Alternating Groups A_5,A_6 and A_7

证明了交错群A5,A6,A7可由其阶和元素的同阶类类数共同刻画.当给定了群的阶和同阶类类数时,通过判断元素的阶之集中所含合数的个数给出了群的素图结构,进而得到群的结构.

In this paper,we demonstrate that the alternating groups A5,A6 and A7can be characterized by the groupsorder and the number of same order elements.When given the groupsorder and the number of same order elements,we can get the prime graph structure of the group by judging the set of the elementsorders which contains the number of the composite numbers,and then get the structure of the group.