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Engel‐4 Groups of Exponent 5
Author(s) -
VaughanLee M
Publication year - 1997
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611597000117
Subject(s) - mathematics , exponent , pure mathematics , linguistics , philosophy
We show that if G is a group of exponent 5, and if G satisfies the Engel‐4 identity [ x,y,y,y,y ]=1, then G is locally finite. By a result of Traustason, this implies that Engel‐4 5‐groups are locally finite. We also show that a group of exponent 5 is locally finite if and only if it satsifies the identity [ x , [ y , z , z , z , z ] , [ y , z , z , z , z ] ] = 1.This result implies that a group of exponent 5 is locally finite if its three generator subgroups are finite. 1991 Mathematics Subject Classification : 20D15, 20F45, 20F50.