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Zvonimir Janko 《Mathematische Zeitschrift》2006,254(1):29-31
In this note we consider finite noncyclic p-groups G all of whose maximal cyclic subgroups X satisfy one of the following two properties.
(a) If each subgroup H of G containing X properly is nonabelian, then p = 2 and G is generalized quaternion.
(b) If X is contained in exactly one maximal subgroup of G, then G is metacyclic.
This solves the problems Nr.1541 and Nr. 1594 from [1]. 相似文献
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Let G be a finite group and Out Col(G) the Coleman outer automorphism group of G(for the definition, see below). The question whether OutCol(G) is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol(G) to be a p′-group are obtained. Our results generalize some well-known theorems. 相似文献
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主要研究子群置换性质对有限群结构的影响.通过子群的置换性得到一类群,即B 群.B群是全可置换群的扩展,利用全可置换群的p次中心扩张和子群的阶得到B群的一些性质并对B 群的结构进行一些刻画.应用B 群的结构得到有限p (p〉2)群为二元生成的B 群的充要条件. 相似文献
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We classify up to isomorphism those finite p-groups,for odd primes p,which contain a cyclic subgroup of index p3. 相似文献
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设$G$是一个群, $X$是$G$的一个子集, 若对于任意$x,y\in X$且$x\neq y$, 都有$xy\neq yx$, 则称$X$是$G$的一个非交换集.
进一步, 如果对于$G$中的任意其它非交换子集$Y$, 都有$|X|\geq|Y|$, 那么称$X$是$G$的一个极大非交换集.
文中确定了Frattini子群循环的有限$p$-\!\!群中极大非交换集和极大Abel子群的势. 相似文献
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Finite p-Groups all of Whose Maximal Subgroups
Either are Metacyclic or Have a Derived
Subgroup of Order ≤ p
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The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko. 相似文献