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CONGRUENCE AND NON-CONGRUENCE SUBGROUPS OF THE (2,3,7)-GROUP

Published online by Cambridge University Press:  06 December 2006

W. W. STOTHERS
W. W. STOTHERS
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, Scotland, U.K. e-mail: [email protected]
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Abstract

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Let $\Delta$ denote the (2,3,7)-group. We establish an upper bound for the number of congruence subgroups of index $n$ and a lower bound for the total number of subgroups of index $n$. Since the latter grows more quickly, there exist non-congruence subgroups of index $n$ for all $n$ greater than some $n_0$.

Keywords

10D0520H10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 351 - 363
Copyright
2006 Glasgow Mathematical Journal Trust