Classifying uniformly generated groups

Research output: Contribution to journalArticle

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Abstract

A finite group G is called uniformly generated, if whenever there is a (strictly ascending) chain of subgroups then d is the minimal number of generators of G. Our main result classifies the uniformly generated groups without using the simple group classification. These groups are related to finite projective geometries by a result of Iwasawa on subgroup lattices.

Original languageEnglish
Number of pages4
JournalCommunications in Algebra
DOIs
Publication statusE-pub ahead of print - 7 Jul 2019

Cite this

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title = "Classifying uniformly generated groups",
abstract = "A finite group G is called uniformly generated, if whenever there is a (strictly ascending) chain of subgroups then d is the minimal number of generators of G. Our main result classifies the uniformly generated groups without using the simple group classification. These groups are related to finite projective geometries by a result of Iwasawa on subgroup lattices.",
keywords = "Length, depth, irredundant, subgroup chain, SUBGROUPS",
author = "Glasby, {S. P.}",
year = "2019",
month = "7",
day = "7",
doi = "10.1080/00927872.2019.1632333",
language = "English",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor & Francis",

}

Classifying uniformly generated groups. / Glasby, S. P.

In: Communications in Algebra, 07.07.2019.

Research output: Contribution to journalArticle

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AU - Glasby, S. P.

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N2 - A finite group G is called uniformly generated, if whenever there is a (strictly ascending) chain of subgroups then d is the minimal number of generators of G. Our main result classifies the uniformly generated groups without using the simple group classification. These groups are related to finite projective geometries by a result of Iwasawa on subgroup lattices.

AB - A finite group G is called uniformly generated, if whenever there is a (strictly ascending) chain of subgroups then d is the minimal number of generators of G. Our main result classifies the uniformly generated groups without using the simple group classification. These groups are related to finite projective geometries by a result of Iwasawa on subgroup lattices.

KW - Length

KW - depth

KW - irredundant

KW - subgroup chain

KW - SUBGROUPS

U2 - 10.1080/00927872.2019.1632333

DO - 10.1080/00927872.2019.1632333

M3 - Article

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

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