On Transitive and Fully Transitive Abelian P-Groups

D. Carroll; Brendan Goldsmith

doi:10.21427/3nrx-b712

On Transitive and Fully Transitive Abelian P-Groups

D. Carroll, Brendan Goldsmith

Technological University Dublin

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

Abstract

It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.

Original language	English
Pages (from-to)	33-41
Journal	Proceedings of the Royal Irish Academy
Volume	96A
Issue number	1
DOIs	https://doi.org/10.21427/3nrx-b712
Publication status	Published - 1 Jan 1996

Keywords

non-transitive
fully transitive
Abelian p-group
finite Ulm subgroups
A.L.S. Corner
cyclic groups
summands

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10.21427/3nrx-b712Licence: CC BY-NC-SA

Cite this

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AB - It is a long standing problem of A.L.S. Corner as to whether there exists a non-transitive fully transitive Abelian p-group with finite Ulm subgroups. The principal result of this paper shows that no such group exists for a special class of p-groups if the Ulm subjgroup is the direct sum of two cyclic groups. Some results on summands of trnsitive and fully transitive groups are obtained.

KW - non-transitive

KW - fully transitive

KW - Abelian p-group

KW - finite Ulm subgroups

KW - A.L.S. Corner

KW - cyclic groups

KW - summands

U2 - 10.21427/3nrx-b712

DO - 10.21427/3nrx-b712

M3 - Article

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SP - 33

EP - 41

JO - Proceedings of the Royal Irish Academy

JF - Proceedings of the Royal Irish Academy

IS - 1

ER -

On Transitive and Fully Transitive Abelian P-Groups

Abstract

Keywords

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