Vol. 26, No. 2, 1968

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Kostrikin’s theorem on Engel groups of prime power exponent

Seymour Bachmuth and Horace Yomishi Mochizuki

Vol. 26 (1968), No. 2, 197–213
Abstract

Theorem Let p 3 be a prime and e 1 any integer. Then there exists a group G which has exponent pe and Engel length e(pe pe1) + (p 3)2.

If e = 1, this reduces to a Theorem of Kostrikin [2], whose proof employed other methods. Our method yields the additional information, that G is a solvable group of class at most k + 1, where k is the least integer such that 2k1 p 2.

Mathematical Subject Classification
Primary: 20.40
Milestones
Received: 14 March 1967
Published: 1 August 1968
Authors
Seymour Bachmuth
Horace Yomishi Mochizuki