ALMOST SIMPLE GROUPS WITH MORE THAN HALF NUMBER OF CYCLIC SUBGROUPS
Let G be a finite group,c(G)be the number of cyclic subgroups of G,and α(G)be the ratio of the number of cyclic subgroups of G to the order of the group,i.e.α(G):= c(G)/|G|.In this paper,it proves that if G is an almost simple group,i.e.S≤G≤Aut(S),in which S is a finite non-abelian simple group,then α(G)≥1/2 if and only if G≌A5,S5,S6.
finite groupsalmost simple groupsnumber of cyclic subgroups
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