On Non-Congruence Subgroups of the Analogue of the Modular Group in Characteristic p
Let k[t] be the polynomial ring over a finite field k. The group SL 2(k[t]) is often referred to as the analogue, in characteristic p, of the classical modular group SL 2(ℤ), where ℤ is the ring of rational integers. It is well-known that the smallest index of a non-congruence subgroup of SL2(ℤ) is 7. Here we compute this index for SL 2(k[t]). (In all but 6 cases it turns out to be 1 + q, where g is the order of k.)
Key wordsSpecial linear group polynomial ring non-congruence subgroup minimal index
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