Asymptotic formulas related to free products of cyclic groups

Author:
Morris Newman

Journal:
Math. Comp. **30** (1976), 838-846

MSC:
Primary 10H25; Secondary 20E30

MathSciNet review:
0466047

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Abstract | References | Similar Articles | Additional Information

Abstract: Asymptotic formulas for the number of subgroups of a given index of the free product of finitely many cyclic groups are given. The classical modular group is discussed in detail, and a table of the number of subgroups of of index *n* is given for .

**[1]**I. M. S. Dey,*Schreier systems in free products*, Proc. Glasgow Math. Assoc.**7**(1965), 61–79 (1965). MR**0188279****[2]**Marshall Hall Jr.,*Subgroups of finite index in free groups*, Canadian J. Math.**1**(1949), 187–190. MR**0028836****[3]**Leo Moser and Max Wyman,*On solutions of 𝑥^{𝑑}=1 in symmetric groups*, Canad. J. Math.**7**(1955), 159–168. MR**0068564**

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1976-0466047-9

Keywords:
Free products,
cyclic groups,
free groups,
classical modular group,
asymptotic formulas,
tables

Article copyright:
© Copyright 1976
American Mathematical Society