Groups with boundedly many commutator of maximal order

Gunnar Traustason; Mercede  Maj; Patrizia  Longobardi; Pavel Shumyatsky

doi:10.1016/j.jalgebra.2020.09.011

Groups with boundedly many commutator of maximal order

Gunnar Traustason, Mercede Maj, Patrizia Longobardi, Pavel Shumyatsky

Department of Mathematical Sciences

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Abstract

By a result of Cocke and Venkataraman we know that if G is a group with at most m elements of maximal order, then is m-bounded. In this paper we consider the following related setting. Suppose G is a group with at most m commutators whose order is maximal among all commutators. What can we say about the structure of the group G?

Original language	English
Pages (from-to)	269-283
Journal	Journal of Algebra
Volume	567
Early online date	14 Sept 2020
DOIs	https://doi.org/10.1016/j.jalgebra.2020.09.011
Publication status	Published - 1 Feb 2021

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title = "Groups with boundedly many commutator of maximal order",

abstract = "By a result of Cocke and Venkataraman we know that if G is a group with at most m elements of maximal order, then is m-bounded. In this paper we consider the following related setting. Suppose G is a group with at most m commutators whose order is maximal among all commutators. What can we say about the structure of the group G?",

author = "Gunnar Traustason and Mercede Maj and Patrizia Longobardi and Pavel Shumyatsky",

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AU - Traustason, Gunnar

AU - Maj, Mercede

AU - Longobardi, Patrizia

AU - Shumyatsky, Pavel

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AB - By a result of Cocke and Venkataraman we know that if G is a group with at most m elements of maximal order, then is m-bounded. In this paper we consider the following related setting. Suppose G is a group with at most m commutators whose order is maximal among all commutators. What can we say about the structure of the group G?

U2 - 10.1016/j.jalgebra.2020.09.011

DO - 10.1016/j.jalgebra.2020.09.011

M3 - Article

SN - 0021-8693

VL - 567

SP - 269

EP - 283

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Groups with boundedly many commutator of maximal order

Abstract

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