Suffix-Connected Languages

Inspired by a series of papers initiated in 2015 Berth\'e et al., we introduce new condition called suffix-connectedness. We show that the groups generated return sets uniformly recurrent suffix-connected language lie single conjugacy class subgroups free group. Moreover, rank this only depends on number connected components extension graph empty word. also how to explicitly compute representative using first order Rauzy graph. Finally, provide an example suffix-connected, contains infinitely many disconnected words.