Ensuring a finite group is supersoluble

R. A. Bryce

doi:10.1017/S0004972700035668

Ensuring a finite group is supersoluble

R. A. Bryce^*

^*Corresponding author for this work

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

5 Citations (Scopus)

Abstract

A special case of the main result is the following. Let G be a finite, non-supersoluble group in which from arbitrary subsets X, Y of cardinality n we can always find x ∈ X and y ∈ Y generating a supersoluble subgroup. Then the order of G is bounded by a function of n. This result is a finite version of one line of development of B.H. Neumann's well-known and much generalised result of 1976 on infinite groups. Copyright Clearance Centre, Inc.

Original language	English
Pages (from-to)	219-226
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	74
Issue number	2
DOIs	https://doi.org/10.1017/S0004972700035668
Publication status	Published - Oct 2006

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title = "Ensuring a finite group is supersoluble",

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N2 - A special case of the main result is the following. Let G be a finite, non-supersoluble group in which from arbitrary subsets X, Y of cardinality n we can always find x ∈ X and y ∈ Y generating a supersoluble subgroup. Then the order of G is bounded by a function of n. This result is a finite version of one line of development of B.H. Neumann's well-known and much generalised result of 1976 on infinite groups. Copyright Clearance Centre, Inc.

AB - A special case of the main result is the following. Let G be a finite, non-supersoluble group in which from arbitrary subsets X, Y of cardinality n we can always find x ∈ X and y ∈ Y generating a supersoluble subgroup. Then the order of G is bounded by a function of n. This result is a finite version of one line of development of B.H. Neumann's well-known and much generalised result of 1976 on infinite groups. Copyright Clearance Centre, Inc.

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DO - 10.1017/S0004972700035668

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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Ensuring a finite group is supersoluble

Abstract

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