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The symmetric genus of sporadic groups


Authors: M. D. E. Conder, R. A. Wilson and A. J. Woldar
Journal: Proc. Amer. Math. Soc. 116 (1992), 653-663
MSC: Primary 20D08
DOI: https://doi.org/10.1090/S0002-9939-1992-1126192-2
MathSciNet review: 1126192
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Abstract: Given a finite group $ G$, the symmetric genus of $ G$ is defined to be the smallest integer $ g$ such that $ G$ acts faithfully on a closed orientable surface of genus $ g$. Previous to this work, the task of determining the symmetric genus for the sporadic simple groups had been completed for all but nine groups: $ {{\text{J}}_3}$, $ \operatorname{McL}$, $ \operatorname{Suz}$, $ {\text{O'N}}$, $ \operatorname{Co}_2$, $ \operatorname{Fi}_{23}$, $ \operatorname{Co}_1$, $ {\text{B}}$, and $ {\text{M}}$. In the present paper the authors resolve the problem for six of these groups, viz. $ {{\text{J}}_3}$, $ \operatorname{McL}$, $ \operatorname{Suz}$, $ {\text{O'N}}$, $ \operatorname{Co}_2$, and $ \operatorname{Co}_1$. Significant progress is also reported for the group $ \operatorname{Fi}_{23}$.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1126192-2
Article copyright: © Copyright 1992 American Mathematical Society

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