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An \(L_2\)-quotient algorithm for finitely presented groups. (English) Zbl 1253.20033
Summary: The paper develops algorithmic methods to enumerate all normal subgroups of a finitely presented group such that the factor groups are either isomorphic to \(\mathrm{PSL}(2,p^n)\) or to \(\mathrm{PGL}(2,p^n)\). The case of two generators is treated in detail. A range of examples starting with the free group on two generators and ending with groups having only finitely many normal subgroups of this type is discussed.

MSC:
20F05 Generators, relations, and presentations of groups
20-04 Software, source code, etc. for problems pertaining to group theory
68W30 Symbolic computation and algebraic computation
Software:
JanetOre; Magma; Janet
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References:
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