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Conjugacy classes and characters for extensions of finite groups

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Abstract

Let H be an extension of a finite group Q by a finite group G. Inspired by the results of duality theorems for étale gerbes on orbifolds, the authors describe the number of conjugacy classes of H that map to the same conjugacy class of Q. Furthermore, a generalization of the orthogonality relation between characters of G is proved.

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Correspondence to Xiang Tang.

Additional information

This work was supported by the National Science Foundation (No. 0900985), the National Security Agency (No. H98230-13-1-0209), the National Science Foundation (No. DMS-0757722) and the Simons Foundation collaboration grant.

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Tang, X., Tseng, HH. Conjugacy classes and characters for extensions of finite groups. Chin. Ann. Math. Ser. B 35, 743–750 (2014). https://doi.org/10.1007/s11401-014-0854-8

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  • DOI: https://doi.org/10.1007/s11401-014-0854-8

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