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On B-injectors of symmetric groups Sₙ and alternating groups Aₙ: a new approach

M. I. AlAli, Bilal Al-Hasanat, I. Sarayreh, M. Kasassbeh, M. Shatnawi, A. Neumann (2009)

Colloquium Mathematicae

The aim of this paper is to introduce the notion of BG-injectors of finite groups and invoke this notion to determine the B-injectors of Sₙ and Aₙ and to prove that they are conjugate. This paper provides a new, more straightforward and constructive proof of a result of Bialostocki which determines the B-injectors of the symmetric and alternating groups.

On chirality groups and regular coverings of regular oriented hypermaps

Antonio Breda d'Azevedo, Ilda Inácio Rodrigues, Maria Elisa Fernandes (2011)

Czechoslovak Mathematical Journal

We prove that if the Walsh bipartite map = 𝒲 ( ) of a regular oriented hypermap is also orientably regular then both and have the same chirality group, the covering core of (the smallest regular map covering ) is the Walsh bipartite map of the covering core of and the closure cover of (the greatest regular map covered by ) is the Walsh bipartite map of the closure cover of . We apply these results to the family of toroidal chiral hypermaps ( 3 , 3 , 3 ) b , c = 𝒲 - 1 { 6 , 3 } b , c induced by the family of toroidal bipartite maps...

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