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Dihedral-like constructions of automorphic loops

Mouna Aboras (2014)

Commentationes Mathematicae Universitatis Carolinae

Automorphic loops are loops in which all inner mappings are automorphisms. We study a generalization of the dihedral construction for groups. Namely, if ( G , + ) is an abelian group, m 1 and α Aut ( G ) , let Dih ( m , G , α ) be defined on m × G by ( i , u ) ( j , v ) = ( i j , ( ( - 1 ) j u + v ) α i j ) . The resulting loop is automorphic if and only if m = 2 or ( α 2 = 1 and m is even). The case m = 2 was introduced by Kinyon, Kunen, Phillips, and Vojtěchovský. We present several structural results about the automorphic dihedral loops in both cases.

Do finite Bruck loops behave like groups?

B. Baumeister (2012)

Commentationes Mathematicae Universitatis Carolinae

This note contains Sylow's theorem, Lagrange's theorem and Hall's theorem for finite Bruck loops. Moreover, we explore the subloop structure of finite Bruck loops.

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