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Quasi-balanced torsion-free groups

H. Pat Goeters, William Ullery (1998)

Commentationes Mathematicae Universitatis Carolinae

An exact sequence 0 A B C 0 of torsion-free abelian groups is quasi-balanced if the induced sequence 0 𝐐 Hom ( X , A ) 𝐐 Hom ( X , B ) 𝐐 Hom ( X , C ) 0 is exact for all rank-1 torsion-free abelian groups X . This paper sets forth the basic theory of quasi-balanced sequences, with particular attention given to the case in which C is a Butler group. The special case where B is almost completely decomposable gives rise to a descending chain of classes of Butler groups. This chain is a generalization of the chain of Kravchenko classes that arise from balanced...

Quasibases of p -groups

Otto Mutzbauer, Elias Toubassi (1999)

Rendiconti del Seminario Matematico della Università di Padova

Quasigroup automorphisms and symmetric group characters

Brent Kerby, Jonathan D. H. Smith (2010)

Commentationes Mathematicae Universitatis Carolinae

The automorphisms of a quasigroup or Latin square are permutations of the set of entries of the square, and thus belong to conjugacy classes in symmetric groups. These conjugacy classes may be recognized as being annihilated by symmetric group class functions that belong to a λ -ideal of the special λ -ring of symmetric group class functions.

Quasigroup covers of division groupoids

Jaroslav J. Ježek, Tomáš Kepka, Petr Němec (2023)

Commentationes Mathematicae Universitatis Carolinae

Let G be a division groupoid that is not a quasigroup. For each regular cardinal α > | G | we construct a quasigroup Q on G × α that is a quasigroup cover of G (i.e., G is a homomorphic image of Q and G is not an image of any quasigroup that is a proper factor of Q ). We also show how to easily obtain quasigroup covers from free quasigroups.

Quasigroups arisen by right nuclear extension

Péter T. Nagy, Izabella Stuhl (2012)

Commentationes Mathematicae Universitatis Carolinae

The aim of this paper is to prove that a quasigroup Q with right unit is isomorphic to an f -extension of a right nuclear normal subgroup G by the factor quasigroup Q / G if and only if there exists a normalized left transversal Σ Q to G in Q such that the right translations by elements of Σ commute with all right translations by elements of the subgroup G . Moreover, a loop Q is isomorphic to an f -extension of a right nuclear normal subgroup G by a loop if and only if G is middle-nuclear, and there exists...

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