Finite groups with non-CYCLIC 2-subgroups which are subnormal or have small indices in their normalizers

Shi J.; Zhang C.

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Finite groups with non-CYCLIC 2-subgroups which are subnormal or have small indices in their normalizers

机译：具有非CYCLIC 2子群的有限群，这些子群为次正规或规范化子中的索引较小

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A new criteria for the solvability of finite groups is obtained. It is proven that a finite group G is always solvable if (i) H is subnormal in G or |N_G(H): H| ≤ 2 for every non-cyclic 2-subgroup H of G that is not a subgroup of Z(G), or (ii) H is subnormal in G or G is A_4-free and |N_G(H): H| ≤ 6 for every non-cyclic 2-subgroup H of G that is not a subgroup of Z(G). Moreover, some new criteria for a finite group being p-nilpotent are also obtained.

机译：获得了有限群可解性的新准则。证明了如果（i）H在G中为次正规或| N_G（H）：H |，则有限群G总是可解的。对于不是Z（G）子集的G的每个非环状2子集H≤2，或者（ii）H在G中为亚正规的，或者G为无A_4的，并且| N_G（H）：H |对于不是Z（G）子集的G的每个非循环2子集H≤6。此外，还获得了关于有限群为p-幂等的一些新准则。

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《Journal of algebra and its applications》 |2013年第4期|共6页
作者
Shi J.; Zhang C.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
index; Non-cyclic 2-subgroup; normalizer; p-nilpotent; subnormal;

机译：指数;非循环2-子群;归一化;p-幂零;次正态;

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专利

1. Finite groups with non-CYCLIC 2-subgroups which are subnormal or have small indices in their normalizers [J] . Shi J., Zhang C. Journal of algebra and its applications . 2013,第4期

机译：具有非CYCLIC 2子群的有限群，这些子群为次正规或规范化子中的索引较小
2. Finite groups with subnormal non-cyclic subgroups [J] . Victor Monakhov, Alexander Trofimuk Journal of group theory . 2014,第5期

机译：具有次正规非循环子群的有限群
3. Normalizers of the Sylow 2-Subgroups in Finite Simple Groups [J] . A. S. Kondratev Mathematical notes . 2005,第3a4期

机译：有限简单群中Sylow 2-子群的归一化
4. Sylow 2-subgroups of finite simple groups [C] . Koichiro Harada, Mong Lung Lang International Conference on Algebra and Their Related Topics . 2003

机译：Sylow 2-有限简单组的子组
5. On Sylow 2-subgroups of finite simple groups of order up to 2(10) [D] . Malyushitsky, Sergey 2004

机译：关于阶为2（10）的有限简单组的Sylow 2子群
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7. Groups with finitely many normalizers of subnormal subgroups [O] . De Mari Fausto, de Giovanni Francesco 2006

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Finite groups with non-CYCLIC 2-subgroups which are subnormal or have small indices in their normalizers

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