西南师范大学学报(自然科学版)
西南師範大學學報(自然科學版)
서남사범대학학보(자연과학판)
JOURNAL OF SOUTHWEST CHINA NORMAL UNIVERSITY
2012年
4期
16-19
,共4页
元素的阶%可刻画的%同阶元长度
元素的階%可刻畫的%同階元長度
원소적계%가각화적%동계원장도
element order%characterizable%the number of elements with the same order
令G为有限群,πe(G)为G的元素的阶的集合,κ∈πe(G),mk表示G中κ阶元的个数,τe(G)= {mk|κ∈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).
令G為有限群,πe(G)為G的元素的階的集閤,κ∈πe(G),mk錶示G中κ階元的箇數,τe(G)= {mk|κ∈πe(G)}.證明L2(27)可用τe(L2(27))加以刻畫,換言之,噹G為群且滿足τe(G)=τe(L2(27))={1,16 383,16 256,341 376,1 040 256,682 752}時,有G(=)L2(27).
령G위유한군,πe(G)위G적원소적계적집합,κ∈πe(G),mk표시G중κ계원적개수,τe(G)= {mk|κ∈πe(G)}.증명L2(27)가용τe(L2(27))가이각화,환언지,당G위군차만족τe(G)=τe(L2(27))={1,16 383,16 256,341 376,1 040 256,682 752}시,유G(=)L2(27).
Let G be a finite group and πe (G) the set of element orders of G.Let κ ∈ πe (G) and mκ be the number of elements of order κ in G.Let τe (G) = {mκ | κ ∈ πe (G) }.In this paper,L2 (27 ) is characterizable by τe (L2 (27 ) ),in other words,if G is a group such that τe(G) = τe(L2(27)) = {1 16 383,16 256,341 376,1 040 256,682 752},then G is isomorphic to L2 (27 ).