Products of groups with finite rank

Amberg, Bernhard

doi:10.1007/bf01194092

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Theorem B Let the Group G = Ab = Ak = Bk With Finite Abelia1

Introduction1

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1988

2019

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Cited by 4 publications

(2 citation statements)

References 8 publications

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“…Theorem B also holds in the case that the group G is soluble and the subgroups A and B have finite abelian section rank. This follows from the Theorem in [7].…”

Section: Theorem B Let the Group G = Ab = Ak = Bk With Finite Abeliamentioning

confidence: 79%

Groups with a nilpotent triple factorisation

Amberg

Franciosi

Giovanni

1988

Bull. Austral. Math. Soc.

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In the investigation of factorised groups one often encounters groups G = AB = AK -BK which have a triple factorisation as a product of two subgroups A and B and a normal subgroup if of G. It is of particular interest to know whether G satisfies some nilpotency requirement whenever the three subgroups A, B and K satisfy this same nilpotency requirement. A positive answer to this problem for the classes of nilpotent, hypercentral and locally nilpotent groups is given under the hypothesis that if is a minimax group or G has finite abelian section rank. The results become false if K has only finite Priifer rank. Some applications of the main theorems are pointed out.

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“…Theorem B also holds in the case that the group G is soluble and the subgroups A and B have finite abelian section rank. This follows from the Theorem in [7].…”

Section: Theorem B Let the Group G = Ab = Ak = Bk With Finite Abeliamentioning

confidence: 79%

Groups with a nilpotent triple factorisation

Amberg

Franciosi

Giovanni

1988

Bull. Austral. Math. Soc.

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“…B. Amberg [3][4][5][6][7][8][9][10][11][12]. In 1989, S. V. Ivanov show that every counable group may be embedded in a product of two Tarski groups [13].…”

Section: Introductionmentioning

confidence: 99%

Product of Periodic Groups

Razzaghmaneshi¹

2019

SARJET

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A group G is called radicable if for each element x of G and for each positive integer n there exists an element y of G such that x=y n. A group G is reduced if it has no non-trivial radicable subgroups. Let the hyper-((locally nilpotent) or finte) group G=AB be the product of two periodic hyper-(abelian or finite) subgroups A and B. Then the following hold: (i) G is periodic. (ii) If the Sylow psubgroups of A and B are Chernikov (respectively: finite, trivial), then the p-component of every abelian normal section of G is Chernikov (respectively: finite, trivial).

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Infinite factorized groups

Amberg

1989

Groups — Korea 1988

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Products of groups with finite rank

Cited by 4 publications

References 8 publications

Groups with a nilpotent triple factorisation

Groups with a nilpotent triple factorisation

Product of Periodic Groups

Infinite factorized groups

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