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Automorphisms of Relatively Free Groups in the Variety N 2 A ∧ AN 2 ∧ N c
Author(s) -
Papistas Athanassios I.
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1017/s0024610701002058
Subject(s) - automorphism , combinatorics , mathematics , automorphism group , rank (graph theory) , variety (cybernetics) , group (periodic table) , discrete mathematics , physics , statistics , quantum mechanics
For positive integers n and c , with n ⩾ 2, let G n , c be a relatively free group of finite rank n in the variety N 2 A ∧ AN 2 ∧ N c . It is shown that the subgroup of the automorphism group Aut( G n , c ) of G n , c generated by the tame automorphisms and an explicitly described finite set of IA‐automorphisms of G n , c has finite index in Aut( G n , c ). Furthermore, it is proved that there are no non‐trivial elements of G n , c fixed by every tame automorphism of G n , c .