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1.
设G是换位子群为p阶群的有限p-群,确定了AutG的结构,证明了(i)AutG/AutGG≌Zp-1,其中AutGG={α∈AutG|α平凡地作用在G上}.(ii)AutGG/Op(AutG)≌iGL(ni,p)×jSp(2mj,p),其中Op(AutG)是AutG的最大正规p-子群,ni和mj由G惟一确定. 相似文献
2.
设G为有限群,称G的子群H为ss-置换子群,如果存在G的次正规子群B使得G=HB,且H与B的任意Sylow子群可以交换,即对任意X∈Syl(B)有XH=HX.利用子群的ss-置换性来研究有限群的结构,得到有限群超可解的两个充分条件. 相似文献
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Mathematical Notes - A subgroup H of a group G is said to be S-quasinormally embedded in G if for every Sylow subgroup P of H, there is an S-quasinormal subgroup K in G such that P is also a Sylow... 相似文献
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A subgroup H of a finite group G is said to be an SS-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. In this paper, we investigate the structure of a group under the assumption that every subgroup with order pm of a Sylow p-subgroup P of G is SS-quasinormal in G for a fixed positive integer m. Some interesting results related to the p-nilpotency and supersolvability of a finite group are obtained. For example, we prove that G is p-nilpo... 相似文献
5.
Czechoslovak Mathematical Journal - A subgroup H of a finite group G is said to be SS-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K is S-quasinormal in K. We... 相似文献
6.
《数学研究通讯:英文版》2016,(3):193-197
Let G be a finite group. A nonempty subset X of G is said to be noncommuting if xy≠yx for any x, y ∈ X with x≠y. If |X| ≥ |Y| for any other non-commuting set Y in G, then X is said to be a maximal non-commuting set. In this paper, we determine upper and lower bounds on the cardinality of a maximal non-commuting set in a finite p-group with derived subgroup of prime order. 相似文献
7.
称有限 p 群 G 为ACT 群,如果对每个交换子群H, 其正规核 HG=1 或 HG=H. 又称p 群 G是CC 群,如果对每个非正规交换子群H, 有 HG=1 或 HG 在G中的指数为 p. 本文分类了ACT 群和CC 群. 相似文献
8.
We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup K of G such that G = HK and H ∩ K ≤ core(H). In this paper it is proved that a finite group G is p-nilpotent if G is S4-free and every minimal subgroup of P n GN is c-supplemented in NG(P), and when p = 2 P is quaternion-free, where p is the smallest prime number dividing the order of G, P a Sylow p-subgroup of G. As some applications of this result, some known results are generalized. 相似文献
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10.
D. R. Prince Williams 《Journal of Mathematical Sciences》2012,183(6):843-854
We introduce a notion of t-fuzzy n-ary subgroup in an n-ary group (G, f) and have studied their related properties. 相似文献