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- W2015887145 abstract "Neumann 19 1 (see also Magnus [ 7 1) and later Tretkoff 1 12 j have stt:died subgroups of the modular group I it is not known a.hether all maxImal nonparabolic subgroups are of this sort (see Magnus [7, p. 121 ]).* Neumann and Tretkoff showed that the Neumann subgroups are associated with what we call tmnsitice triples (a: A, B): A and R arc permutations of a (necessarily countable) infinite set I2 such that A’ = B’ = i and that C =AB is transitive on R. A knowledge of ali such Lrlpics 1’: equivalent to a knowledge of all Neumann subgroups. Morcovcr. Tretkofr obtained, by the Reidemeister-Schreier process, a presentaticn for S expressed very simply in terms of an associated triple (a: ‘4. L3). From :h: well known fact that :M is the free product of a group of order 2 with a group of order 3, it follows from the Kurosh Subgroup Theorem Lhal S is the fret product of r; groups of order 2, rI groups of order 3, and r-L infinite cyclic groups, for certain numbers r,, 0 < r, < oc, (we write CG for EC,,). ‘I‘retkotj obtained partial information about the numbers rz, r3, r,r . Tretkoffs work prompted us to study the set of transitive triples (Q. .$I: R:t." @default.
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- W2015887145 date "1982-08-01" @default.
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- W2015887145 title "Nonparabolic subgroups of the modular group" @default.
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- W2015887145 doi "https://doi.org/10.1016/0021-8693(82)90255-1" @default.
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