A sharply 2-transitive group without a non-trivial abelian normal subgroup

Eliyahu Rips; Yoav Segev; Katrin Tent

doi:10.4171/JEMS/730

A sharply 2-transitive group without a non-trivial abelian normal subgroup

Eliyahu Rips, Yoav Segev, Katrin Tent

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We show that any group G is contained in some sharply 2-transitive group G without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups G that we construct have no fixed points.

Original language	English
Pages (from-to)	2895-2910
Number of pages	16
Journal	Journal of the European Mathematical Society
Volume	19
Issue number	10
DOIs	https://doi.org/10.4171/JEMS/730
State	Published - 1 Jan 2017

Keywords

Free product
HNN extension
Malnormal
Sharply 2-transitive

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.4171/JEMS/730

Cite this

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title = "A sharply 2-transitive group without a non-trivial abelian normal subgroup",

abstract = "We show that any group G is contained in some sharply 2-transitive group G without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups G that we construct have no fixed points.",

keywords = "Free product, HNN extension, Malnormal, Sharply 2-transitive",

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AU - Segev, Yoav

AU - Tent, Katrin

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PY - 2017/1/1

Y1 - 2017/1/1

N2 - We show that any group G is contained in some sharply 2-transitive group G without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups G that we construct have no fixed points.

AB - We show that any group G is contained in some sharply 2-transitive group G without a non-trivial abelian normal subgroup. This answers a long-standing open question. The involutions in the groups G that we construct have no fixed points.

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KW - HNN extension

KW - Malnormal

KW - Sharply 2-transitive

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JO - Journal of the European Mathematical Society

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A sharply 2-transitive group without a non-trivial abelian normal subgroup

Abstract

Keywords

ASJC Scopus subject areas

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