Hyper-(rank one) groups

Francesco de Giovanni; Martin L. Newell

doi:10.1007/s11587-013-0145-9

Hyper-(rank one) groups

Francesco de Giovanni, Martin L. Newell

Mathematics

University of Naples Federico II

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

A group G is called a P₁-group if it has a normal series of finite length whose factors have rank 1, while G is an H₁-group if it has an ascending normal series of the same type. This paper investigates properties of P₁-groups and H₁-groups which correspond to known properties of nilpotent and supersoluble groups.

Original language	English
Pages (from-to)	117-126
Number of pages	10
Journal	Ricerche di Matematica
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s11587-013-0145-9
Publication status	Published - Jun 2013

Keywords

Fitting property
Rank one group
Schur property

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10.1007/s11587-013-0145-9

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title = "Hyper-(rank one) groups",

abstract = "A group G is called a P1-group if it has a normal series of finite length whose factors have rank 1, while G is an H1-group if it has an ascending normal series of the same type. This paper investigates properties of P1-groups and H1-groups which correspond to known properties of nilpotent and supersoluble groups.",

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AU - de Giovanni, Francesco

AU - Newell, Martin L.

PY - 2013/6

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N2 - A group G is called a P1-group if it has a normal series of finite length whose factors have rank 1, while G is an H1-group if it has an ascending normal series of the same type. This paper investigates properties of P1-groups and H1-groups which correspond to known properties of nilpotent and supersoluble groups.

AB - A group G is called a P1-group if it has a normal series of finite length whose factors have rank 1, while G is an H1-group if it has an ascending normal series of the same type. This paper investigates properties of P1-groups and H1-groups which correspond to known properties of nilpotent and supersoluble groups.

KW - Fitting property

KW - Rank one group

KW - Schur property

UR - https://www.scopus.com/pages/publications/84878454870

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DO - 10.1007/s11587-013-0145-9

M3 - Article

AN - SCOPUS:84878454870

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VL - 62

SP - 117

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JO - Ricerche di Matematica

JF - Ricerche di Matematica

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ER -

Hyper-(rank one) groups

Abstract

Keywords

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