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We describe, in a constructive way, a family of commutative loops of odd order, $n \geq 7$ , which have no nontrivial subloops and whose multiplication group is isomorphic to the alternating group $𝒜_{n}$ .

Commutative zeropotent semigroups

Václav Flaška, Tomáš Kepka (2006)

Acta Universitatis Carolinae. Mathematica et Physica

Commutative zeropotent semigroups with few invariant congruences

Robert El Bashir, Tomáš Kepka (2008)

Czechoslovak Mathematical Journal

Commutative semigroups satisfying the equation $2 x + y = 2 x$ and having only two $G$ -invariant congruences for an automorphism group $G$ are considered. Some classes of these semigroups are characterized and some other examples are constructed.

Commutative zeropotent semigroups with few prime ideals

Jaroslav Ježek, Tomáš Kepka, P. Němec (2011)

Commentationes Mathematicae Universitatis Carolinae

We construct an infinite commutative zeropotent semigroup with only two prime ideals.

Commutativity Criterions using Normal Subgroup Lattices

Simion Breaz (2009)

Rendiconti del Seminario Matematico della Università di Padova

Commutativity in groups presented by finite Church-Rosser Thue systems

Klaus Madlener, Friedrich Otto (1988)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Commutativity of Operators on the Lattice of Existence Varieties.

Norman R. Reilly, Shuhua Zhang (1997)

Monatshefte für Mathematik

Commutativity of the Schur algebra.

Teicher, Mina (1997)

Beiträge zur Algebra und Geometrie

Commutativity theorems for rings and groups with constraints on commutators.

Psomopoulos, Evagelos (1984)

International Journal of Mathematics and Mathematical Sciences

Commutator length of finitely generated linear groups.

Sanati, Mahboubeh Alizadeh (2008)

International Journal of Mathematics and Mathematical Sciences

Commutator subgroups of the extended Hecke groups $\bar{H} (λ_{q})$

Recep Şahin, Osman Bizim, I. N. Cangul (2004)

Czechoslovak Mathematical Journal

Hecke groups $H (λ_{q})$ are the discrete subgroups of $P S L (2, ℝ)$ generated by $S (z) = - {(z + λ_{q})}^{- 1}$ and $T (z) = - \frac{1}{z}$ . The commutator subgroup of $H$ ( $λ_{q})$ , denoted by $H^{'} (λ_{q})$ , is studied in [2]. It was shown that $H^{'} (λ_{q})$ is a free group of rank $q - 1$ . Here the extended Hecke groups $\bar{H} (λ_{q})$ , obtained by adjoining $R_{1} (z) = 1 / \bar{z}$ to the generators of $H (λ_{q})$ , are considered. The commutator subgroup of $\bar{H} (λ_{q})$ is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the $H (λ_{q})$ case, the index of $H^{'} (λ_{q})$ is changed by $q$ , in the case of $\bar{H} (λ_{q})$ , this number is either 4 for...

Commutators and associators in Catalan loops

Jan M. Raasch (2010)

Commentationes Mathematicae Universitatis Carolinae

Various commutators and associators may be defined in one-sided loops. In this paper, we approximate and compare these objects in the left and right loop reducts of a Catalan loop. To within a certain order of approximation, they turn out to be quite symmetrical. Using the general analysis of commutators and associators, we investigate the structure of a specific Catalan loop which is non-commutative, but associative, that appears in the original number-theoretic application of Catalan loops.

Commutators and squares in free groups.

Sarkar, Sucharit (2004)

Algebraic & Geometric Topology

Commutators and squares in free nilpotent groups.

Akhavan-Malayeri, Mehri (2009)

International Journal of Mathematics and Mathematical Sciences

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