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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On finite groups containing three $ CC$-subgroups


Authors: Zvi Arad and Pamela Ferguson
Journal: Proc. Amer. Math. Soc. 80 (1980), 27-33
MSC: Primary 20D06; Secondary 20C15
MathSciNet review: 574503
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Abstract: A finite group G has a self-centralization system of type $ (2\vert{A_1}\vert,4\vert{A_2}\vert,4\vert{A_3}\vert)$ if G contains three nonconjugate CC-subgroups $ {A_1},{A_2},{A_3}$, such that $ \vert{N_G}({A_1})\vert = 2\vert{A_1}\vert,\vert{N_G}({A_2})\vert = 4\vert{A_2}\vert,\vert{N_G}({A_3})\vert = 4\vert{A_3}\vert$. The authors prove that if a finite group G has a self-centralization system of type $ (2\vert{A_1}\vert,4\vert{A_2}\vert,4\vert{A_3}\vert)$ and $ \vert G\vert \leqslant 3\vert{A_1}{\vert^2}\vert{A_2}{\vert^2}\vert{A_3}{\vert^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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DOI: https://doi.org/10.1090/S0002-9939-1980-0574503-0
Article copyright: © Copyright 1980 American Mathematical Society