0000000001037621
AUTHOR
F.j. Vera-lópez
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…
The exact bounds for the degree of commutativity of a p-group of maximal class, I
Abstract The first major study of p-groups of maximal class was made by Blackburn in 1958. He showed that an important invariant of these groups is the ‘degree of commutativity.’ Recently (1995) Fernandez-Alcober proved a best possible inequality for the degree of commutativity in terms of the order of the group. Recent computations for primes up to 43 show that sharper results can be obtained when an additional invariant is considered. A series of conjectures about this for all primes have been recorded in [A. Vera-Lopez et al., preprint]. In this paper, we prove two of these conjectures.