Abstract
Let G be a finite group, c(G) the number of its cyclic subgroups, and \(\alpha (G)=c(G)/|G|\). Set \(I(G)=|\{g\in G|g^2=1\}|\). In this paper we prove if \(\alpha (G)=3/4\), then G is isomorphic to a direct product of an elementary abelian 2-group and a dihedral group \(D_{16}, D_{24}\), or a group satisfying \(I({G})=\frac{1}{2}|{G}|\) and \(\exp ({G})=4\).
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Project supported by the NSF of China (Grant No. 12161035).
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Communicated by K. N. Raghavan.
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Gao, X., Shen, R. Finite groups with many cyclic subgroups. Indian J Pure Appl Math 54, 485–498 (2023). https://doi.org/10.1007/s13226-022-00270-5
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DOI: https://doi.org/10.1007/s13226-022-00270-5