Product of two groups with nilpotent subgroups of index at most 2

Монахов, В. С.

doi:10.1007/bf01669433

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…Theorem 2.1 [7]. Let the group G = G 1 G 2 be the product of the subgroups G 1 and G 2 such that there exists a subgroup H i with |G i : H i | 2 (i = 1, 2).…”

Section: If G/o P (G) Is Of Even Order Then G/o P (G) Is Supersolvabmentioning

confidence: 97%

Some sufficient conditions for a finite group to be supersolvable

Asaad

Монахов

2011

Acta Math Hung

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“…Theorem 2.1 [7]. Let the group G = G 1 G 2 be the product of the subgroups G 1 and G 2 such that there exists a subgroup H i with |G i : H i | 2 (i = 1, 2).…”

Section: If G/o P (G) Is Of Even Order Then G/o P (G) Is Supersolvabmentioning

confidence: 97%

Some sufficient conditions for a finite group to be supersolvable

Asaad

Монахов

2011

Acta Math Hung

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“…It should be noted that the structure of the finite group G = AB satisfying the hypothesis of the theorem was investigated by B. Huppert [3], W. Scott [6] and V. Monakhov [4,5]. In particular, it was shown in [4] that G is soluble in this case.…”

Section: Introductionmentioning

confidence: 99%

Products of two groups containing cyclic subgroups of index at most 2

Amberg

Sysak²

2008

Arch. Math.

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It is proved that every group of the form G = AB with subgroups A and B each of which has a cyclic subgroup of index at most 2 is metacyclicby-finite. Mathematics Subject Classification (2000). Primary 20D40.Keywords. Products of groups, metacyclic group, dihedral group. Introduction.Let the group G = AB be the product of two subgroups A and B, i.e. G = {ab | a ∈ A, b ∈ B}. It seems intuitively clear that the structure of the group G should somehow be determined by that of the factors A and B. For instance, if A and B are abelian, then G is metabelian by a well-known theorem of N. Ito [1, Theorem 2.1.1] obtained more that fifty years ago. Note that almost all results concerning the structure of the group G = AB with infinite abelian subgroups A and B are based on this theorem. One of the first is due to P. Cohn [2] who proved that in the case of infinite cyclic subgroups A and B there exists a non-trivial normal subgroup of G which is contained in A or B. This implies in particular that G has a subgroup H of finite index whose derived subgroup H and the factor group H/H are both cyclic, in other words, G is metacyclic-by-finite.

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Finite groups

Кондратьев¹,

Махнев²,

Starostin³

1989

J Math Sci

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The present survey is formed primarily on the basis of works reviewed in the Referativnyi Zhurnal "Matematika" during 1976-1983 and is a continuation of surveys of the same name published in 1966, 1971, 1976 in the series "Albegra, Topologiya, Geometriya" (INT). Principal attention is devoted to finite simple groups and their classification.The present survey is formed primarily on the basis of works reviewed in RZh "Matematika" during 1976-1983 and is a continuation of surveys of the same title of A. I. Kostrikin [162], So A. Chunikhin, L. A. Shemetkov [371], and V. D. Mazurov [194]. Rapid development of the theory of finite groups was observed during this period. More than 2000 papers were published and also the books [

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Product of two groups with nilpotent subgroups of index at most 2

Cited by 3 publications

References 8 publications

Some sufficient conditions for a finite group to be supersolvable

Some sufficient conditions for a finite group to be supersolvable

Products of two groups containing cyclic subgroups of index at most 2

Finite groups

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