Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 2 of 2
Full-Text Articles in Physical Sciences and Mathematics
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Non-Solvable Groups All Of Whose Indices Are Odd-Square-Free, Sajjad Mahmood Robati, Roghayeh Hafezieh Balaman
Turkish Journal of Mathematics
Given a finite group $G$ and $x\in G$, the class size of $x$ in $G$ is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if $G$ is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of $G$, which is an answer to the dual of the question mentioned by Huppert in [5].
On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n
On The Extended Hecke Groups \Overline{H}(\Lambda _Q), Ni̇hal Yilmaz Özgür, Recep Şahi̇n
Turkish Journal of Mathematics
Hecke groups H(\lambda _q) have been studied extensively for many aspects in the literature, [5], [8]. The Hecke group H(\lambda_3), the modular group PSL(2, \Bbb{Z} ) , has especially been of great interest in many fields of mathematics, for example number theory, automorphic function theory and group theory. In this paper we consider the extended Hecke groups \overline{H}(\lambda _q) which are defined analogously with the extended modular group. We find the conjugacy classes of torsion elements in \overline{H}(\lambda _q). Using this we give some results about the normal subgroups and Fuchsian subgroups of \overline{H}(\lambda _q).