Displaying similar documents to “Sharply 2-transitive sets of permutations and groups of affine projectivities.”

Units in group rings of crystallographic groups

Karel Dekimpe (2003)

Fundamenta Mathematicae

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In [3], the authors initiated a technique of using affine representations to study the groups of units of integral group rings of crystallographic groups. In this paper, we use this approach for some special classes of crystallographic groups. For a first class of groups we obtain a normal complement for the group inside the group of normalized units. For a second class of groups we show that the Zassenhaus conjectures ZC1 and ZC3 are valid. This generalizes the results known for the...

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

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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.