Schreier loops
We study systematically the natural generalization of Schreier's extension theory to obtain proper loops and show that this construction gives a rich family of examples of loops in all traditional common, important loop classes.
Schreier type theorems for bicrossed products
We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then...
Soluble products of nilpotent groups
Soluble Products of Polycyclic Groups.
Soluble products of two locally finite groups with min- for every prime
Some Groups with Non-Trivial Multiplicators.
Some properties of generalized wreath products
Some Remarks about Multiplicators and Finitely Presented Groups.
Splitting Theorems and Engel Groups.
Subgroups with projective abelianization and trivial multiplicator.
Sur certaines extensions de
Dans cet article, on étudie certaines extensions scindées et non scindées des groupes unitaires , pour , sur le corps par des -groupes extra-spéciaux. Les extensions ainsi obtenues sont des groupes de -transpositions, on en donne des présentations fischériennes.