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Typical Frobenius coverings

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Abstract

A covering p from a Cayley graph Cay(G, X) onto another Cay(H, Y) is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p: G → H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay(H, Y). We show that any typical Frobenius covering Cay(G, X) of Cay(H, Y) can be derived from an epimorphism \( \tilde f \) from G to H which is determined by an automorphism f of H. If Cay(G, X 1) and Cay(G, X 2) are two isomorphic typical Frobenius coverings under a graph isomorphism ϕ, some properties satisfied by ϕ are given.

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Authors and Affiliations

  1. Department of Mathematics, Yan Tai University, Yan Tai, 264005, P. R. China

    Yan Wang

  2. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P. R. China

    Rong Quan Feng

  3. Department of Mathematics, Yeungnam University, Kyongsan, 712-749, Korea

    Jaeun Lee

Authors
  1. Yan Wang
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  2. Rong Quan Feng
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  3. Jaeun Lee
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Corresponding author

Correspondence to Yan Wang.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 10571005 and 10801114), Natural Science Foundation of Shandong Province (Grant No. Y2007A30) and Shan Dong Domestic Visiting Project

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Wang, Y., Feng, R.Q. & Lee, J. Typical Frobenius coverings. Acta. Math. Sin.-English Ser. 26, 2209–2214 (2010). https://doi.org/10.1007/s10114-010-7630-9

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  • DOI: https://doi.org/10.1007/s10114-010-7630-9

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