Lohrey, Markus
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Lohrey, Markus
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Publication Access status: Metadata only , Subgroup Membership in GL(2,Z)(2023)It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all group elements are represented by so-called power words, i.e., words of the form $p_1^{z_1} p_2^{z_2} \cdots p_k^{z_k}$. Here the $p_i$ are explicit words over the generating set of the group and all $z_i$ are binary encoded integers. As a corollary, it follows that the subgroup membership problem for the matrix group $\textsf{GL}(2,\mathbb {Z})$ can be decided in polynomial time when elements of $\textsf{GL}(2,\mathbb {Z})$ are represented by matrices with binary encoded integers. For the same input representation, it also shown that one can compute in polynomial time the index of a given finitely generated subgroup of $\textsf{GL}(2,\mathbb {Z})$.Source Type:Article3
