Subgroup Membership in GL(2,Z)

Abstract It is shown that the subgroup membership problem for a virtually free group can be decided in polynomial time when all elements are represented by so-called power words, i.e., words of form $$p_1^{z_1} p_2^{z_2} \cdots p_k^{z_k}$$ p 1 z 2 ⋯ k . Here $$p_i$$ i explicit over generating set and $$z_i$$ binary encoded integers. As corollary, it follows matrix $$\textsf{GL}(2,\mathbb {Z})$$ GL ( , Z ) matrices with For same input representation, also one compute index given finitely generated