‘On Sets of Pp-Generators of Finite Groups’

Krempa, Jan; Stocka, Agnieszka

doi:10.1017/s0004972715001148

Bull. Aust. Math. Soc.

2015

DOI: 10.1017/s0004972715001148

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‘On Sets of Pp-Generators of Finite Groups’

Jan Krempa¹,

Agnieszka Stocka²

Abstract: This note completes the proof of the structure theorem for pp-matroid groups which was stated in our earlier paper J. Krempa and A. Stocka [‘On sets of pp-generators of finite groups’, Bull. Aust. Math. Soc.91 (2015), 241–249].

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2020

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Sets of prime power order generators of finite groups

Stocka

2020

ADM

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A subset X of prime power order elements of a finite group G is called pp-independent if there is no proper subset Y of X such that Y, Φ(G) = X, Φ(G) , where Φ(G) is the Frattini subgroup of G. A group G has property B pp if all pp-independent generating sets of G have the same size. G has the pp-basis exchange property if for any pp-independent generating sets B 1 , B 2 of G and x ∈ B 1 there exists y ∈ B 2 such that (B 1 \ {x}) ∪ {y} is a ppindependent generating set of G. In this paper we describe all finite solvable groups with property B pp and all finite solvable groups with the pp-basis exchange property.

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Sets of prime power order generators of finite groups

Stocka

2020

ADM

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‘On Sets of Pp-Generators of Finite Groups’

Abstract: This note completes the proof of the structure theorem for pp-matroid groups which was stated in our earlier paper J. Krempa and A. Stocka [‘On sets of pp-generators of finite groups’, Bull. Aust. Math. Soc.91 (2015), 241–249].

Cited by 1 publication

References 4 publications

Sets of prime power order generators of finite groups

Sets of prime power order generators of finite groups

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