用τe(L2(25))刻画L2(25)

摘要

Let G be a group and πe (G) the set of element orders of G. Suppose that Te (G) ={ mk | k ∈πe(G) } , where mk is the number of elements of order k in G. In this paper we prove that L2 (25) is characterizable by τe (L2 (25)), in other words, if G is a group such that τe (G) =τe(L2(25)) = {1, 1 023, 992, 4 960, 15 840, 9 920}, then G is isomorphic to L2(25).%设G是一个群,πe(G)为G的元素的阶的集合.令τe(G)={ mk|k∈πe(G)},这里mk为G的k阶元的个数.我们证明了L2(25)可以用τe(L2(25))刻画.换言之,如果G是群,并且满足τe(G)=τe(L2(25))={1,1 023,992,4 960,15 840,9 920},那么G≌L2(25).