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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A characterization of odd order extensions of the finite projective symplectic groups $ {\rm PSp}(4,\,q)$


Author: Morton E. Harris
Journal: Trans. Amer. Math. Soc. 163 (1972), 311-327
MSC: Primary 20.75
DOI: https://doi.org/10.1090/S0002-9947-1972-0286897-4
MathSciNet review: 0286897
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Abstract: In a recent paper, W. J. Wong characterized the finite projective symplectic groups $ {\text{PSp}}(4,q)$ where $ q$ is a power of an odd prime integer by the structure of the centralizer of an involution in the center of a Sylow $ 2$-subgroup of $ {\text{PSp}}(4,q)$. In the present paper, finite groups which contain an involution in the center of a Sylow $ 2$-subgroup whose centralizer has a more general structure than in the $ {\text{PSp}}(4,q)$ case are classified by showing them to be odd ordered extensions of $ {\text{PSp}}(4,q)$.


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DOI: https://doi.org/10.1090/S0002-9947-1972-0286897-4
Keywords: Centralizer of an involution, projective symplectic groups, simple group, odd ordered extension
Article copyright: © Copyright 1972 American Mathematical Society