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On lattice automorphisms of the special linear group

Mauro Costantini (1989)

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

We show, with a counterexample, that proposition 3 in [2], as it stands, is not correct; we prove however that by changing the hypothesis the thesis of the proposition remains still valid.

On lattice properties of S-permutably embedded subgroups of finite soluble groups

L. M. Ezquerro, M. Gómez-Fernández, X. Soler-Escrivà (2005)

Bollettino dell'Unione Matematica Italiana

In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and H Hall π ( G ) such that H V Hall π ( V ) and 1 H U Hall π ( U ) . Suppose also H U is a Hall π-sub-group of some S-permutable subgroup of G. Then H U V Hall π ( U V ) and H U , H V Hall π ( U V ) . Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders permute.

On left C - 𝒰 -liberal semigroups

Yong He, Fang Shao, Shi-qun Li, Wei Gao (2006)

Czechoslovak Mathematical Journal

In this paper the equivalence 𝒬 ˜ U on a semigroup S in terms of a set U of idempotents in S is defined. A semigroup S is called a 𝒰 -liberal semigroup with U as the set of projections and denoted by S ( U ) if every 𝒬 ˜ U -class in it contains an element in U . A class of 𝒰 -liberal semigroups is characterized and some special cases are considered.

On left distributive left idempotent groupoids

Přemysl Jedlička (2005)

Commentationes Mathematicae Universitatis Carolinae

We study the groupoids satisfying both the left distributivity and the left idempotency laws. We show that they possess a canonical congruence admitting an idempotent groupoid as factor. This congruence gives a construction of left idempotent left distributive groupoids from left distributive idempotent groupoids and right constant groupoids.

On L-Groups.

David B. Wales, Hans J. Zassenhaus (1972)

Mathematische Annalen

On Lie semiheaps and ternary principal bundles

Andrew James Bruce (2024)

Archivum Mathematicum

We introduce the notion of a Lie semiheap as a smooth manifold equipped with a para-associative ternary product. For a particular class of Lie semiheaps we establish the existence of left-invariant vector fields. Furthermore, we show how such manifolds are related to Lie groups and establish the analogue of principal bundles in this ternary setting. In particular, we generalise the well-known ‘heapification’ functor to the ambience of Lie groups and principal bundles.

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