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Free centre‐by‐nilpotent‐by‐abelian groups
Author(s) -
Johnson Marianne,
Stöhr Ralph
Publication year - 2009
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdp041
Subject(s) - mathematics , nilpotent , abelian group , nilpotent group , pure mathematics , torsion (gastropod) , prime (order theory) , torsion subgroup , central series , order (exchange) , combinatorics , algebra over a field , elementary abelian group , medicine , surgery , finance , economics
We prove that the free centre‐by‐(nilpotent‐of‐class‐( c − 1))‐by‐abelian groups F /[γ c ( F ′), F ] are torsion‐free for c = 6. This is in startling contrast to the cases when c is a prime and when c = 4, where these relatively free groups contain non‐trivial elements of finite order.