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12.29 (1992)

Open

Classify the locally finite groups for which the augmentation ideal of the complex group algebra is a simple ring. The problem goes back to I. Kaplansky (1965).

Contributor: A. E. Zalesskiĭ

Progress

For partial results, see (K. Bonvallet, B. Hartley, D. S. Passman, M. K. Smith, Proc. Amer. Math. Soc., 56, no. 1 (1976), 79–82; A. E. Zalesskiĭ, Algebra i Analiz, 2, no. 6 (1990), 132–149 (Russian); Ch. Praeger, A. E. Zalesskii, Proc. London Math. Soc., 70, no. 2 (1995), 313–335; B. Hartley, A. Zalesski, J. London Math. Soc., 55 (1997), 210–230).

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