proper subgroup 中文意思是什麼
proper subgroup
解釋
真子群-
Theorem 2. 4 let g be a non - abelian inner - finite group, each non - trivial proper subgroup of g is prime order cyclic group if and only if g is a simple group ; each proper subgroup of g is nilpotent ; and each non - trivial subgroup of g is self - normalizer
4設g是非阿貝爾的內有限群，則g的每個非平凡真子群都是素數階循環群的充分必要條件是g是單群， g的每個真子群冪零且g的每個非平凡的真子群自正規化定理2 -
Theorem 2. 5 let g be an infinite simple group that satisfies maximal condition. g is an inner - finite group and each non - trivial proper subgroup of g is abelian if and only if for each x in g, cg ( x ) is the only maximal subgroup that contain x. s * ( a *, c * ) - groups can be regarded as a generalizations of dedekind groups, since all of dedekind groups are s * ( a *, c * ) - groups
5設g是滿足極大條件的無限單群，則g是內有限群，而且g的每個非平凡真子群是阿貝爾群的充分必要條件是對g的任意非平凡元x ，有c _ g （ x ）是g的含x的唯一極大子群且c _ g （ x ）是有限的。
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