On subgroups of finite p-groups

被引:9
作者
Berkovich, Yakov [1 ]
Janko, Zvonimir [2 ]
机构
[1] Univ Haifa Mt Carmel, Dept Math, IL-31905 Haifa, Israel
[2] Univ Heidelberg, Math Inst, D-69120 Heidelberg, Germany
关键词
2-GROUPS;
D O I
10.1007/s11856-009-0038-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In A 2, we prove that if a 2-group G and all its nonabelian maximal sub-groups are two-generator, then G is either metacyclic or minimal non-abelian. In A 3, we consider a similar question for p > 2. In A 4 the 2-groups all of whose minimal nonabelian subgroups have order 16 and a cyclic subgroup of index 2, are classified. It is proved, in A 5, that if G is a nonmetacyclic two-generator 2-group and A, B, C are all its maximal subgroups with d(A) a parts per thousand currency sign d(B) a parts per thousand currency sign d(C), then d(C) = 3 and either d(A) = d(B) = 3 (this occurs if and only if G/G' has no cyclic subgroup of index 2) or else d(A) = d(B) = 2. Some information on the last case is obtained in Theorem 5.3.
引用
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页码:29 / 49
页数:21
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