Classifying uniformly generated groups

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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

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