Finite 2-Groups with Small Centralizer of an Involution, 2
Finite 2-Groups with Small Centralizer of an Involution, 2
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DOI：
10.1006/jabr.2001.8753
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发表时间：
2001-07
影响因子：
0.9
通讯作者：
Z. Janko
中科院分区：
文献类型：
--
作者：
Z. Janko
本文对具有对合t ∈ G的有限2-群G进行了分类. 2：m使得C t t Q，其中Q Q是2阶广义四元数G 2群，m 3.从一开始，就很清楚这样的群G不可能是极大类的。然后，根据已知的结果，G必包含正规4-子群U。根据t U或t U，我们有两种本质上不同的可能性。。。在第一种情况下，其中t U第2节，我们有C t G或G，G的阶等于2 m2，然后我们得到四类2-群，将给出的生成元和关系。。在第二种情况下，其中t U第3节，情况更加复杂，因为G的阶不受参数m的限制。在
In this paper we classify finite 2-groups G which possess an involution t Ž . 2 : m such that C t t Q, where Q Q is a generalized quaternion G 2 group of order 2 , m 3. From the start, it is clear that such a group G cannot be of maximal class. Then, by the known results, G must contain a normal 4-subgroup U. We have two essentially different possibilities according to t U or t U. Ž . Ž . In the first case, where t U Section 2 , we have either C t G or G the order of G is equal to 2 m 2 and then we get four classes of 2-groups which will be given in terms of generators and relations. Ž . In the second case, where t U Section 3 , the situation is more complicated since the order of G is not bounded with the parameter m. In