Normal Subgroups and Elements of H`(lq)

Authors : İsmail Naci CANGÜL

Pages : 251-256

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this study, we consider the normal subgroups of H`insert ignore into journalissuearticles values(lq);, where Hinsert ignore into journalissuearticles values(lq); denotes the Hecke groups. After recalling some results from [2], particularly on the group structure and on the relations with the power subgroups of Hinsert ignore into journalissuearticles values(lq);, the even subgroup Heinsert ignore into journalissuearticles values(lq); of Hinsert ignore into journalissuearticles values(lq); is discussed. It is shown that H`insert ignore into journalissuearticles values(lq); is a normal subgroup of Heinsert ignore into journalissuearticles values(lq); with index q. For this reason each subgroup of H`insert ignore into journalissuearticles values(lq); consists of only even elements. H``insert ignore into journalissuearticles values(lq); is also considered and it is concluded that it is the normal subgroup of H`insert ignore into journalissuearticles values(lq); generated by all commutators of the elements of H`insert ignore into journalissuearticles values(lq);. Using the Kurosh subgroup theorem, the group structure of normal subgroups of Hinsert ignore into journalissuearticles values(lq); can be found to be free groups. Their ranks are given in terms of the index.
Keywords : Turk J Math, 23, 1999, , 251 256 Turk J Math, vol 23, iss 2