0000000001037622
AUTHOR
R. Esteban-romero
The exact bounds for the degree of commutativity of a p-group of maximal class, II
AbstractLet G be a p-group of maximal class. Since the pioneer work of Blackburn in 1958 (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92]), several authors have obtained information about the degree of commutativity c of G, in order to precise which the defining relations of G are (cf. [N. Blackburn, Acta Math. 100 (1958) 45–92; R. Shepherd, PhD Thesis, University of Chicago, 1970; C.R. Leedham-Green, S. McKay, Quart. J. Math. Oxford Ser. (2) 27 (1976) 297–311, Quart. J. Math. Oxford Ser. (2) 29 (1978) 175–186, 281–299; G.A. Fernández-Alcober, J. Algebra 174 (1995) 523–530; A. Vera-López, J.M. Arregi, F.J. Vera-López, Comm. Algebra 23 (1995) 2765–2795, Math. Proc. Cambridge Philos. Soc. 122…
Triply Factorised Groups and the Structure of Skew Left Braces
The algebraic structure of skew left brace has proved to be useful as a source of set-theoretic solutions of the Yang–Baxter equation. We study in this paper the connections between left and right $$\pi $$ -nilpotency and the structure of finite skew left braces. We also study factorisations of skew left braces and their impact on the skew left brace structure. As a consequence of our study, we define a Fitting-like ideal of a left brace. Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.