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In this paper some infinitely based varieties of groups are constructed and these results are transferred to the associative algebras (or Lie algebras) over an infinite field of an arbitrary positive characteristic.

Infinite locally soluble $k$ -Engel groups

Lucia Serena Spiezia (1992)

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

In this paper we deal with the class $E_{k}^{*}$ of groups $G$ for which whenever we choose two infinite subsets $X$ , $Y$ there exist two elements $x \in X$ , $y \in Y$ such that $[x, \underset{k}{\underset{︸}{y, \dots, y}}] = 1$ . We prove that an infinite finitely generated soluble group in the class $E_{k}^{*}$ is in the class $E_{k}$ of $k$ -Engel groups. Furthermore, with $k = 2$ , we show that if $G \in E_{2}^{*}$ is infinite locally soluble or hyperabelian group then $G \in E_{2}$ .

Inverse semigroup varieties with the amalgamation property.

T.E. Hall (1978)

Semigroup forum

Just Non-Metabelian Groups.

Jay I. Miller (1979)

Mathematische Zeitschrift

$l$ -многообразия без независимого базиса тождеств

N.Ya. Medvedev (1982)

Mathematica Slovaca

$ℓ$ -многообразия без независимого базиса тождеств. II.

N.Ya. Medvedev (1985)

Mathematica Slovaca

Monoid varieties defined by xn+1 = ... are local.

P.R. Jones (1993)

Semigroup forum

Near-Rings of Polynomials over ...-Groups.

Günter Pilz, Yong-Sian So (1981)

Monatshefte für Mathematik

Nilpotent, weakly abelian and Hamiltonian lattice ordered groups

Norman R. Reilly (1983)

Czechoslovak Mathematical Journal

Nonfree projectives in products of group varieties

V. Artamonov (1982)

Banach Center Publications

Nonsplitting F-quasigroups

Stephen Gagola III (2012)

Commentationes Mathematicae Universitatis Carolinae

T. Kepka, M.K. Kinyon and J.D. Phillips: The structure of F-quasigroups, J. Algebra 317 (2007), no. 2, 435–461 developed a connection between F-quasigroups and NK-loops. Since NK-loops are contained in the variety generated by groups and commutative Moufang loops, a question that arises is whether or not there exists a nonsplit NK-loop and likewise a nonsplit F-quasigroup. Here we prove that there do indeed exist nonsplit F-quasigroups and show that there are exactly four corresponding nonsplit...

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Homogeneous models and generic extensions.

Hyperidentities and hypervarieties.

Hyperidentities of groups and semigroups.

Hyperidentities of groups and semigroups. (Short Communication).

Identifying and distinguishing various varieties of abelian topological groups [Book]

Infinite independent systems of the identities of the associative algebra over an infinite field of characteristic $p > 0$