On finite groups containing three cc-subgroups

Zvi Arad; Pamela Ferguson

doi:10.1090/S0002-9939-1980-0574503-0

On finite groups containing three cc-subgroups

Zvi Arad
, Pamela Ferguson

University of Miami

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

1 Scopus citations

Abstract

A finite group G has a self-centralization system of type (2|A₁|, 4|A₂|,4|A₃|) if G contains three nonconjugate CC-subgroups A₁, A₂, A₃, such that|N_G(A₁)| = 2|A₁|,|N_G(A₂)| = 4|A₂|,|N_G(A₃)| = 4|A₃| The authors prove that if a finite group G has a self-centralization system of type (2|A₁|, 4|A₂|, 4|,4₃|) and|G| < 3| A₁,|²| A₂|²| A₃|², then G has a nilpotent normal subgroup N such that G/N is isomorphic to Sz(q) for suitable q.

Original language	English
Pages (from-to)	27-33
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	80
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1980-0574503-0
State	Published - Sep 1980
Externally published	Yes

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title = "On finite groups containing three cc-subgroups",

abstract = "A finite group G has a self-centralization system of type (2|A1|, 4|A2|,4|A3|) if G contains three nonconjugate CC-subgroups A1, A2, A3, such that|NG(A1)| = 2|A1|,|NG(A2)| = 4|A2|,|NG(A3)| = 4|A3| The authors prove that if a finite group G has a self-centralization system of type (2|A1|, 4|A2|, 4|,43|) and|G| < 3| A1,|2| A2|2| A3|2, then G has a nilpotent normal subgroup N such that G/N is isomorphic to Sz(q) for suitable q.",

author = "Zvi Arad and Pamela Ferguson",

year = "1980",

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doi = "10.1090/S0002-9939-1980-0574503-0",

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T1 - On finite groups containing three cc-subgroups

AU - Arad, Zvi

AU - Ferguson, Pamela

PY - 1980/9

Y1 - 1980/9

N2 - A finite group G has a self-centralization system of type (2|A1|, 4|A2|,4|A3|) if G contains three nonconjugate CC-subgroups A1, A2, A3, such that|NG(A1)| = 2|A1|,|NG(A2)| = 4|A2|,|NG(A3)| = 4|A3| The authors prove that if a finite group G has a self-centralization system of type (2|A1|, 4|A2|, 4|,43|) and|G| < 3| A1,|2| A2|2| A3|2, then G has a nilpotent normal subgroup N such that G/N is isomorphic to Sz(q) for suitable q.

AB - A finite group G has a self-centralization system of type (2|A1|, 4|A2|,4|A3|) if G contains three nonconjugate CC-subgroups A1, A2, A3, such that|NG(A1)| = 2|A1|,|NG(A2)| = 4|A2|,|NG(A3)| = 4|A3| The authors prove that if a finite group G has a self-centralization system of type (2|A1|, 4|A2|, 4|,43|) and|G| < 3| A1,|2| A2|2| A3|2, then G has a nilpotent normal subgroup N such that G/N is isomorphic to Sz(q) for suitable q.

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SP - 27

EP - 33

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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On finite groups containing three cc-subgroups

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