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Finite simple monogenic entropic quasigroups with quasi-identity

100%

Bińczak G. , Kaleta J.

Demonstratio Mathematica

2011

tom Vol. 44, nr 1

17-27

In this paper we describe finite simple monogenic entropic quasigroups with quasi-identity.

Some finite directly indecomposable non-monogenic entropic quasigroups with quasi-identity

100%

Bińczak G. , Kaleta J.

Discussiones Mathematicae - General Algebra and Applications

2014

tom 34

nr 1

5-26

In this paper we show that there exists an infinite family of pairwise non-isomorphic entropic quasigroups with quasi-identity which are directly indecomposable and they are two-generated.

Cyclic entropic quasigropups

100%

Bińczak G. , Kaleta J.

Demonstratio Mathematica

2009

tom Vol. 42, nr 2

269-281

In this paper we explain the relationship of some entropic quasigroups to abelian groups with involution. It is known that (Zn, -n) are examples of cyclic entropic quasigroups which are not groups. We describe all cyclic entropic quasigroups with quasiidentity.

Finite directly indecomposable monogenic entropic quasigroups with quasi-identity

100%

Bińczak G. , Kaleta J.

Demonstratio Mathematica

2012

tom Vol. 45, nr 3

519-532

In this paper we characterize finite directly indecomposable monogenic entropic quasigroups with quasi-identity.

No cutoff for circulants : an elementary proof

100%

Abrams A. , Landau H. , Pommersheim J. , Babson E. , Landau Z.

Probability and Mathematical Statistics

2022

tom Vol. 42, Fasc. 1

97--108

We give an elementary proof of a result due to Diaconis and Saloff-Coste (1994) that families of symmetric simple random walks on Cayley graphs of abelian groups with a bound on the number of generators never have sharp cutoff. Here convergence to the stationary distribution is measured in the total variation norm. This is a situation of bounded degree and no expansion; sharp cutoff (or the cutoff phenomenon) has been shown to occur in families such as random walks on a hypercube (Diaconis, 1996) in which the degree is unbounded as well as on a random regular graph where the degree is fixed, but there is expansion (Diaconis and Saloff-Coste, 1993).

Conjoinability in Pregroups

88%

Kiślak-Malinowska A.

Fundamenta Informaticae

2004

tom Vol. 61, nr 1

29--36

Pregroups are introduced by Lambek as a framework for syntactic analysis of Natural Language; they are algebraic models of Compact Bilinear Logic. In the present paper we consider the problem of conjoinability in the calculus of pregroups. We show that two types are conjoinable in a pregroup iff they are equal in a free group. This result is analogous to Pentus' characterization of conjoinability in the Lambek calculus.

On m-ω1-pω+n - projective abelian p-groups

51%

Danchev P.

Demonstratio Mathematica

2014

tom Vol. 47, nr 4

805--825

For any non-negative integers m and n, we define the classes of m-ω1-pω+n -projective groups and strongly m-ω1-pω+n -projective groups, which properly encompass the classes of ω1-pω+n -projectives introduced by Keef in J. Algebra Numb. Th. Acad. (2010) and strongly ω1-pω+n -projectives introduced by the present author in Hacettepe J. Math. Stat. (2014), respectively. The new group structures share many interesting properties, which are closely related to these of the aforementioned two own subclasses. Moreover, certain basic results in this direction are also established.