On elements of order 2 in the free centre-by-(nilpotent of class 3)-by-abelian group within the variety of all soluble groups of derived length 3
S Kesim
article (Uluslararası, Hakemli) | Yazar(lar): S Kesim | Yıl: 2021 | Dergi/Kurum: COMMUNICATIONS IN ALGEBRA | İndeks: WOS.SCI | DOI: 10.1080/00927872.2021.1894165 | Anahtar Kelimeler: Free central extensions of groups, Homology of groups — Özet: Let F be a free group of rank d >= 2. Consider the quotient F/[gamma(4)(F '
Let F be a free group of rank d >= 2. Consider the quotient F/[gamma(4)(F '),F]F ''', the free centre-by-(nilpotent of class 3)-by-abelian group within the variety of all soluble groups of derived length 3. A peculiar feature of this group is the occurence of torsion in its centre. Our main result is a complete description of an elementary abelian 2-group of rank (d/4) in F/[gamma(4)(F '),F]F ''' in terms of generators of F for d >= 4. Our approach makes essential use of homological methods.