The local stationary presentation of the alternating groups and the normal form

Abstract

We give the canonical normal form for the elements of the finite or infinite alternating groups using local stationary presentation of these groups.

Alternating subgroups of Coxeter groups and their spinor extensions

“…. The Coxeter-Todd algorithm given in Section 4 provides a normal form, different from the normal form in [12], for the elements of the group A + n .…”

“…The presentation ( 14) is a local and stationary, in the sense of [11], presentation for the chain of groups A + n . In [12] a presentation of the group A + n is proved. The generators are ρ 1 , .…”

“…53, 117924 Moscow, Russia For type A our presentations of the chains of the groups A + n and Ã+ n are local and stationary. For the chain of the groups A + n a similar (but not exactly the same) presentation was given in [12] and it was asked there how to generalize this presentation to all alternating groups. For types B and D, our presentations of the chains of groups B + n , B+ n , D + n and D+ n are local and eventually stationary (that is, stationary for n n 0 for a certain n 0 ).…”