Kostrikin’s theorem on Engel groups of prime power exponent

Seymour Bachmuth and Horace Yomishi Mochizuki

Vol. 26 (1968), No. 2, 197–213

DOI: 10.2140/pjm.1968.26.197

Abstract

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

Mathematical Subject Classification

Primary: 20.40

Milestones

Received: 14 March 1967

Published: 1 August 1968