On a graph related to permutability in finite groups

A. Ballester-Bolinches; John Cossey; R. Esteban-Romero

doi:10.1007/s10231-009-0124-7

On a graph related to permutability in finite groups

A. Ballester-Bolinches^*, John Cossey, R. Esteban-Romero

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which Γ(G) is complete.

Original language	English
Pages (from-to)	567-570
Number of pages	4
Journal	Annali di Matematica Pura ed Applicata
Volume	189
Issue number	4
DOIs	https://doi.org/10.1007/s10231-009-0124-7
Publication status	Published - 2010

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title = "On a graph related to permutability in finite groups",

abstract = "For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which Γ(G) is complete.",

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author = "A. Ballester-Bolinches and John Cossey and R. Esteban-Romero",

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T1 - On a graph related to permutability in finite groups

AU - Ballester-Bolinches, A.

AU - Cossey, John

AU - Esteban-Romero, R.

PY - 2010

Y1 - 2010

N2 - For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which Γ(G) is complete.

AB - For a finite group G we define the graph Γ(G) to be the graph whose vertices are the conjugacy classes of cyclic subgroups of G and two conjugacy classes A, B are joined by an edge if for some A ∈ A, B ∈ B A and B permute. We characterise those groups G for which Γ(G) is complete.

KW - Finite groups

KW - Graphs

KW - Permutability

KW - Soluble groups

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U2 - 10.1007/s10231-009-0124-7

DO - 10.1007/s10231-009-0124-7

M3 - Article

SN - 0373-3114

VL - 189

SP - 567

EP - 570

JO - Annali di Matematica Pura ed Applicata

JF - Annali di Matematica Pura ed Applicata

IS - 4

ER -

On a graph related to permutability in finite groups

Abstract

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