Abstract
The problems discussed in this book bring us quite often to counting congruence subgroups in an arithmetic group Γ = G(ℤ), and that leads to counting primes. One may note that if G is the one-dimensional unipotent algebraic group G a , then G(ℤ) = ℤ and counting primes is actually counting maximal subgroups in this G(ℤ). So the whole content of this book can be considered as a generalization of the counting problems studied in analytic number theory. From this point of view, one may see our subject of subgroup growth as a chapter of “non-commutative analytic number theory”.
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© 2003 Birkhäuser Verlag
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Lubotzky, A., Segal, D. (2003). Primes. In: Subgroup Growth. Progress in Mathematics, vol 212. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-8965-0_27
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DOI: https://doi.org/10.1007/978-3-0348-8965-0_27
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-9846-1
Online ISBN: 978-3-0348-8965-0
eBook Packages: Springer Book Archive