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- W2024256799 abstract "In the Kourovka Notebook, Deaconescu asks if |AutG| > φ(|G|) for all finite groups G, where φ denotes the Euler totient function; and whether G is cyclic whenever |AutG| = φ(|G|). In an earlier paper we have answered both questions in the negative, and shown that |AutG|/φ(|G|) can be made arbitrarily small. Here we show that these results remain true if G is restricted to being perfect, or soluble. 1. The question, and general overview Let φ denote the Euler totient function, so that φ(n) is the number of integers m with 1 6 m 6 n such that m and n are coprime, and φ(n) n = r ∏" @default.
- W2024256799 created "2016-06-24" @default.
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- W2024256799 date "2006-01-01" @default.
- W2024256799 modified "2023-09-27" @default.
- W2024256799 title "On the orders of automorphism groups of finite groups. II" @default.
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- W2024256799 doi "https://doi.org/10.1515/jgt.2006.036" @default.
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