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7.48 (1980)

Solved

(Well-known problem). Suppose that, in a finite group $G$, each two elements of the same order are conjugate. Is then $|G| \leqslant 6$?

Contributor: S. A. Syskin

Progress

Yes, it is, mod CFSG (P. Fitzpatrick, Proc. Roy. Irish Acad. Sect. A, 85, no. 1 (1985), 53–58); see also (W. Feit, G. Seitz, Illinois J. Math., 33, no. 1 (1988), 103–131) and (R. W. van der Waall, A. Bensaïd, Simon Stevin, 65 (1991), 361–374).

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