用τ_e(L_2(2~7))刻画L_2(2~7)(英文)

Characterization of L_2(2~7) by τ_e(L_2(2~7))

令G为有限群,πe(G)为G的元素的阶的集合,k∈πe(G),mk表示G中k阶元的个数,τe(G)={mk|k∈πe(G)}.证明L2(27)可用τe(L2(27))加以刻画,换言之,当G为群且满足τe(G)=τe(L2(27))={1,16 383,16 256,341 376,1 040 256,682 752}时,有G■L2(27).

Let G be a finite group and πe（G） the set of element orders of G.Let k∈πe（G） and mk be the number of elements of order k in G.Let τe（G）={mk ｜k∈πe（G）}.In this paper,L2（2^7） is characterizable by τe（L2（2^7））,in other words,if G is a group such that τe（G）=τe（L2（2^7））={1,16 383,16 256,341 376,1 040 256,682 752},then G is isomorphic to L2（2^7）.