Let g and h be two distinct elements of a group G, and let n be a positive integer. Consider a sequence w=(w1,w2,…) which is not eventually periodic and where each wi is either g or h. Denote by H the subgroup of G generated by all elements of the form wkwk+1…wk+n−1 with k≥1. Prove that H does not depend on the choice of the sequence w (but may depend on n). group theoryabstract algebraCombinatorics of wordssubgroupSequences