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An infinite group with subgroups of prime orders

A. Yu. Ol'shanskii


Abstract: An infinite nonabelian group all of whose proper subgroups have prime order is constructed. This solves a problem of O. Yu. Schmidt. The proof involves modifying and extending the series of lemmas in an earlier paper of the author.
Bibliography: 3 titles.

UDC: 512

MSC: Primary 20F10; Secondary 03D40

Received: 20.12.1978

 English version: Mathematics of the USSR-Izvestiya, 1981, 16:2, 279–289

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