Hirsch Number and Pr{üfer Rank

HasFiniteRank(G): GrpMat -> BoolElt

This function takes as input a finitely generated matrix group \(G\) defined over \(Q\) or a number field, and determines if it has finite Hirsch number and Prüfer rank. If so, it returns true, else false.

HirschNumber(G): GrpMat -> RngIntElt

This function takes as input a finitely generated finite rank matrix group \(G\) defined over \(Q\) or a number field, and returns its Hirsch number.

HasFiniteIndex(G, H): GrpMat, GrpMat -> BoolElt

If the subgroup \(H\) has finite index in the soluble-by-finite matrix group \(G\) defined over \(Q\) or a number field, then this function returns true, else it returns false. It decides this by checking whether \(G\) and \(H\) have identical Hirsch numbers.

PrueferRankBound(G): GrpMat -> BoolElt

This function takes as input a finitely generated finite rank matrix group \(G\) defined over \(Q\) or a number field, and returns an upper bound to its Prüfer rank.