The symmetric genus of sporadic groups

Conder, M. D. E.; Wilson, R. A.; Woldar, A. J.

doi:10.1090/S0002-9939-1992-1126192-2

The symmetric genus of sporadic groups
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by M. D. E. Conder, R. A. Wilson and A. J. Woldar PDF

Proc. Amer. Math. Soc. 116 (1992), 653-663 Request permission

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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