Let GGG be a group and SSS some subset of GGG. A group word in SSS is an expression of the form s1ℓ1s2ℓ2⋯snℓns_1^{\ell_1}s_2^{\ell_2}\cdots s_n^{\ell_n}s1ℓ1s2ℓ2⋯snℓn where si∈Ss_i \in Ssi∈S and ℓi=±1\ell_i = \pm 1ℓi=±1.