| 关于一个猜想的探讨 |
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| 引用本文： | 袁香环. 关于一个猜想的探讨[J]. 新疆大学学报(理工版), 1987, 0(4) |
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| 作者姓名： | 袁香环 |
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| 摘 要： | 作者在文献[1]中证明了一个结果:有限群G如果满足|P(G),p|=1,则G为P~-可解群。本文将指出,这个论断的逆命题不成立。并且还指出,满足条件(|P(G)|,p)=1的有限群也不一定是p~-超可解群。
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| 关 键 词： | 猜想 有限群 P~-可解群 |
ON A GUESS |
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| Yuan Xianghuan. ON A GUESS[J]. Journal of Xinjiang University(Science & Engineering), 1987, 0(4) |
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| Authors: | Yuan Xianghuan |
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| Affiliation: | Yuan Xianghuan |
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| Abstract: | After proving the following results in[1].1. If a finite group G satisfies (|P(G)|,p)=1, then G is a p-solvable group. 2. If a finite group G is p-supersolvable, then (|P(G)|,p)=1,The Auther of[1] has ever guessed:"If a finite group G is p-solvable, then(|P(G)|,p)=1". In this paper, a contraexample is constructed, Furthemore a class of finite groups between p-supersolvable aud p-solvable is offered. |
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| Keywords: | guess finite group p-solvable group |
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