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Some divisibility properties of the subgroup counting function for free products

1992
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Mathematics of Computation
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Let G be the free product of finitely many cyclic groups of prime order. Let M" denote the number of subgroups of G of index n . Let Cp denote the cyclic group of order p, and C* the free product of k cyclic groups of order p . We show that Mn is odd if C\ occurs as a factor in the free product decomposition of G. We also show that if C\ occurs as a factor in the free product decomposition of G and if C2 is either not present or occurs to an even power, then Mn = 0 mod 3 if and only if n = 2

doi:10.1090/s0025-5718-1992-1106969-8
fatcat:ovhzj7ziw5dfrnqi4msev2uxvy