AUTOMORPHISMS OF PARTIALLY COMMUTATIVE GROUPS II: COMBINATORIAL SUBGROUPS

作者：Duncan Andrew J^*; Remeslennikov Vladimir N

来源：International Journal of Algebra and Computation, 2012, 22(7): 1250074.

DOI：10.1142/S0218196712500749

• Artin groups
• automorphism groups of groups

We define several %26quot;standard%26quot; subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decomposition of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilizing a certain lattice of %26quot;admissible subsets%26quot; of the vertices of C. We then characterize those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.

• 出版日期2012-11