Geodesic
Examples of groups with the same number of subgroups of every index
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 95-99

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In this note we show that certain non-isomorphic free amalgamated products with cyclic amalgamated subgroup and the same type have the same number of subgroups of every index.
Keywords: non-isomorphic free amalgamated products. 
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Chris W. Parker; Atapattu A. C. Kanchana. Examples of groups with the same number of subgroups of every index. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 7 (2014) no. 1, pp. 95-99. http://geodesic.mathdoc.fr/item/JSFU_2014_7_1_a9/