Vol. 50, No. 1, 1974

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On the Engel margin

Tommy Kay Teague

Vol. 50 (1974), No. 1, 205–214

The marginal subgroup for any outer commutator word has been characterized by R. F. Turner-Smith. This paper considers the marginal subgroup E(G) of G for the Engel word e2(x,y) = [x,y,y] of length two. The principal result is that an element a of G is in E(G) if and only if [x,y,a][a,y,x] is a law in G. The method of proof relies upon properties of Engel elements established by W. Kappe.

Among other results are the following: (a) E(G)∕Z2(G) is an elementary Abelian 3-group of central automorphisms on the commutator subgroup G. (b) If Z(G) γ3(G) has no elements of order 3 or if Gis Cernikov complete, then E(G) = Z2(G). (c) If [G : E(G)] = m is finite, then the verbal subgroup e2(G) is finite with order dividing a power of m.

Mathematical Subject Classification 2000
Primary: 20F10
Received: 29 August 1972
Published: 1 January 1974
Tommy Kay Teague