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We consider the extended Hecke groups H ( q/ generated by T . ́/D 1 =  ́, S. ́/D 1=. ́C q/ and R. ́/D 1=  ́ with q D 2cos. =q/ for q 3 integer: In this article, we study the abstract group structures of the power subgroupsH m ( q/ ofH ( q/ for each positive integer m. Then, we give the relations between commutator subgroups and power subgroups. 2010 Mathematics Subject Classification: 20H10; 11F06

Power subgroups of the extended Hecke groups