Turkish Journal of Mathematics
Abstract
In this study, we consider the normal subgroups of H^{'}(\lambda_q), where H(\lambda_q) denotes the Hecke groups. After recalling some results from [2], particularly on the group structure and on the relations with the power subgroups of H(\lambda_q), the even subgroup H_e(\lambda_q) of H(\lambda_q) is discussed. It is shown that H^{'}(\lambda_q) is a normal subgroup of H_e(\lambda_q) with index q. For this reason each subgroup of H^{'}(\lambda_q) consists of only even elements. H^{''}(\lambda_q) is also considered and it is concluded that it is the normal subgroup of H^{'}(\lambda_q) generated by all commutators of the elements of H^{'}(\lambda_q). Using the Kurosh subgroup theorem, the group structure of normal subgroups of H(\lambda_q) can be found to be free groups. Their ranks are given in terms of the index.
DOI
-
First Page
251
Last Page
256
Recommended Citation
CANGÜL, İSMAİL NACİ (1999) "Normal Subgroups and Elements of H^{'}(\lambda_q)," Turkish Journal of Mathematics: Vol. 23: No. 2, Article 3. Available at: https://journals.tubitak.gov.tr/math/vol23/iss2/3
