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Test sets in free metabelian Lie algebras.

Chirkov, I. V., Shevelin, M. A. (2002)

Sibirskij Matematicheskij Zhurnal

The Hughes subgroup

Robert Bryce (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$ . Hughes [3] made the following conjecture: if $H_{p} (G)$ is non-trivial, its index in $G$ is at most $p$ . There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p = 3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common proof is...

The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra.

Kabanov, A.N. (2009)

Sibirskij Matematicheskij Zhurnal

The number of sides of a parallelogram.

Falbel, Elisha, Koseleff, Pierre-Vincent (1999)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

The small index property for algebras.

Chirkov, I.V. (2000)

Siberian Mathematical Journal

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

Abanina, L., Mishchenko, S. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30Let F be a field of characteristic zero. In this paper we study the variety of Leibniz algebras 3N determined by the identity x(y(zt)) ≡ 0. The algebras of this variety are left nilpotent of class not more than 3. We give a complete description of the vector space of multilinear identities in the language of representation theory of the symmetric group Sn and Young diagrams. We also show that the...

Transitive Hall sets.

Duchamp, Gérard, Flouret, Marianne, Luque, Jean-Gabriel (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Trees, free right-symmetric algebras, free Novikov algebras and identities.

Dzhumaldil'daev, Askar, Löfwall, Clas (2002)

Homology, Homotopy and Applications

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