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Third Engel groups

Published online by Cambridge University Press:  17 April 2009

N. D. Gupta  and
M. F. Newman
N. D. Gupta
Affiliation:
Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
M. F. Newman
Affiliation:
Mathematics Research Section Institute of Advanced Studies School of Mathematical SciencesAustralian National UniversityCanberra, ACT 2601Australia
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Abstract

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We present some new results on third Engel groups which are motivated by computer calculations but are not dependent on them. They include:

• for n > 2 every n-generator third Engel group is nilpotent of class at most 2n – 1;

• the fifth term of the lower central series of a third Engel group has exponent dividing 20;

• the subgroup generated by fifth powers of elements in a third Engel group is nearly centre-by-metabeliami;

and a normal form theorem for freest third Engel groups without elements of order 2.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 40 , Issue 2 , October 1989 , pp. 215 - 230
Copyright
Copyright © Australian Mathematical Society 1989

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