Finite equilibrated 2-generated 2-groups
Finite equilibrated 2-generated 2-groups
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DOI：
10.1007/s10474-006-0004-1
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发表时间：
2006-01
影响因子：
0.9
通讯作者：
G. Silberberg
中科院分区：
文献类型：
--
作者：
G. Silberberg
如果G的子群H不能写成H的两个非正规子群的乘积，则称一个群为平衡群。Blackburn，Deaconescu和Mann [1]研究了有限平衡群，给出了不可解群的完整描述。另一方面，他们证明了有限幂零群的平衡性仅取决于它的2-生成p-子群的结构。因此，所有的有限2-生成的平衡p-群都被分类为任何奇素数，但casep=2仍然没有解决。这一特殊情况将是本文件的主题。
A group is calledequilibratedif no subgroupHofGcan be written as a product of two non-normal subgroups of H. Blackburn, Deaconescu and Mann [1] investigated the finite equilibrated groups, giving a complete description of the non-soluble ones. On the other hand, they showed that the property of a finite nilpotent group of being equilibrated depends solely on the structure of its 2-generatedp-subgroups. Consequently, all the finite 2-generated equilibratedp-groups were classified for any odd primep,but the casep=2 remained unsolved. This special case will represent the subject of the present paper.