An L2-quotient algorithm for finitely presented groups on arbitrarily many generators

Abstract

We generalize the Plesken-Fabiańska ${\mathrm{L}}_2$-quotient algorithm for finitely presented groups on two or three generators to allow an arbitrary number of generators. The main difficulty lies in a constructive description of the invariant ring of $\mathrm{GL}(2,K)$ on $m$ copies of $\mathrm{SL}(2,K)$ by simultaneous conjugation. By giving this description, we generalize and simplify some of the known results in invariant theory. An implementation of the algorithm is available in the computer algebra system Magma.

arXiv comment21 pages

References in corpus (1)

• Determining Aschbacher classes using characters

Cited by in corpus (1)

• Universal Covers of Finite Groups