Subgroups of finite index in a free product with amalgamated subgroup

Author:
W. W. Stothers

Journal:
Math. Comp. **36** (1981), 653-662

MSC:
Primary 20E06; Secondary 10D07, 20E07

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606522-9

MathSciNet review:
606522

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Abstract: Let *G* be a free product of finitely many finite groups with amalgamated subgroup. Using coset diagrams, a recurrence relation is obtained for the number of subgroups, and of free subgroups, of each finite index in *G*. In the latter case, an asymptotic formula is derived. When the amalgamated subgroup is central, the relation takes a simpler form.

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DOI:
https://doi.org/10.1090/S0025-5718-1981-0606522-9

Article copyright:
© Copyright 1981
American Mathematical Society