2017/06/29 by Andrew J. Duncan, Duncan, Andrew J., Vladimir N. Remeslennikov +1
Mathematics · #20F05 (Secondary) #20F28 (Primary) #20F36 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F05 #msc:20F28 #msc:20F36
paper · pdf · doi:10.48550/arxiv.1706.09517
36 pages, 2 figures
arxiv created 2017/06/29 · arxiv updated 2017/06/30
The structure of a certain subgroup S of the automorphism group of a partially commutative group (RAAG) G is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of the generators of G, and show that S is the subgroup of automorphisms which fix all subgroups ⟨ Y⟩ of G, for all admissible subsets Y. A decomposition of S as an iterated tower of semi-direct products in given and the structure of the factors of this decomposition described. The construction allows a presentation of S to be computed, from the commutation graph of G.