Search results for "20F05"
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On presentations for mapping class groups of orientable surfaces via Poincaré's Polyhedron theorem and graphs of groups
2021
The mapping class group of an orientable surface with one boundary component, S, is isomorphic to a subgroup of the automorphism group of the fundamental group of S. We call these subgroups algebraic mapping class groups. An algebraic mapping class group acts on a space called ordered Auter space. We apply Poincaré's Polyhedron theorem to this action. We describe a decomposition of ordered Auter space. From these results, we deduce that the algebraic mapping class group of S is a quotient of the fundamental group of a graph of groups with, at most, two vertices and, at most, six edges. Vertex and edge groups of our graph of groups are mapping class groups of orientable surfaces with one, tw…
Some considerations on the nonabelian tensor square of crystallographic groups
2011
The nonabelian tensor square $G\otimes G$ of a polycyclic group $G$ is a polycyclic group and its structure arouses interest in many contexts. The same assertion is still true for wider classes of solvable groups. This motivated us to work on two levels in the present paper: on a hand, we investigate the growth of the Hirsch length of $G\otimes G$ by looking at that of $G$, on another hand, we study the nonabelian tensor product of pro--$p$--groups of finite coclass, which are a remarkable class of solvable groups without center, and then we do considerations on their Hirsch length. Among other results, restrictions on the Schur multiplier will be discussed.