TY - JOUR
T1 - Filtrations of free groups arising from the lower central series
AU - Chapman, Michael
AU - Efrat, Ido
N1 - Funding Information:
This work was supported by the Israel Science Foundation (grants No. 23/09 and 152/13). It is partially based on the M.Sc. thesis of the first author done under the supervision of the second author in Ben-Gurion University of the Negev.
Publisher Copyright:
© 2016 by De Gruyter.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - We make a systematic study of filtrations of a free group F defined as products of powers of the lower central series of F. Under some assumptions on the exponents, we characterize these filtrations in terms of the group algebra, the Magnus algebra of non-commutative power series, and linear representations by upper-triangular unipotent matrices. These characterizations generalize classical results of Grün, Magnus, Witt, and Zassenhaus from the 1930s, as well as later results on the lower p-central filtration and the p-Zassenhaus filtrations. We derive alternative recursive definitions of such filtrations, extending results of Lazard. Finally, we relate these filtrations to Massey products in group cohomology.
AB - We make a systematic study of filtrations of a free group F defined as products of powers of the lower central series of F. Under some assumptions on the exponents, we characterize these filtrations in terms of the group algebra, the Magnus algebra of non-commutative power series, and linear representations by upper-triangular unipotent matrices. These characterizations generalize classical results of Grün, Magnus, Witt, and Zassenhaus from the 1930s, as well as later results on the lower p-central filtration and the p-Zassenhaus filtrations. We derive alternative recursive definitions of such filtrations, extending results of Lazard. Finally, we relate these filtrations to Massey products in group cohomology.
UR - http://www.scopus.com/inward/record.url?scp=84969508648&partnerID=8YFLogxK
U2 - 10.1515/jgth-2016-0508
DO - 10.1515/jgth-2016-0508
M3 - Article
AN - SCOPUS:84969508648
VL - 19
SP - 405
EP - 433
JO - Journal of Group Theory
JF - Journal of Group Theory
SN - 1433-5883
IS - 3
ER -