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On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

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

It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.

On Mikheev's construction of enveloping groups

J. I. Hall (2010)

Commentationes Mathematicae Universitatis Carolinae

Mikheev, starting from a Moufang loop, constructed a groupoid and reported that this groupoid is in fact a group which, in an appropriate sense, is universal with respect to enveloping the Moufang loop. Later Grishkov and Zavarnitsine gave a complete proof of Mikheev's results. Here we give a direct and self-contained proof that Mikheev's groupoid is a group, in the process extending the result from Moufang loops to Bol loops.

On minimal ideals in semigroups with respect to their subsets. I.

Imrich Abrhan (1997)

Mathematica Bohemica

In the paper, the following concept are defined: (i) a minimal left (right, two-sided) ideal with respect to a subset B of a semigroup S , (ii) a kernel with respect to a subset B of a semigroup S , and their basic properties are investigated.

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