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9.34 (1984)

Solved

(S. K. Grosser, W. N. Herfort). Does there exist an infinite compact $p$-group in which the centralizers of all elements are finite?

Contributor: Yu. N. Mukhin

Progress

No, it does not exist, in view of the connection of this problem with the Restricted Burnside Problem (S. K. Grosser, W. N. Herfort, Trans. Amer. Math. Soc., 283, no. 1 (1984), 211–224) and because of the positive solution to the latter (E. I. Zel’manov, Math. USSR–Izv., 36 (1991), 41–60; Math. USSR–Sb., 72 (1992), 543–565).

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