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Varieties of groups of exponent 4

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Abstract

It is proved that the variety of all 4-Engel groups of exponent 4 is a maximal proper subvariety of the Burnside variety B-4, and the consequences of this are discussed for the finite basis problem for varieties of groups of exponent 4. It is proved that, for r greater than or equal to 2, the 4-Engel verbal subgroup of the r-generator Burnside group B(r, 4) is irreducible as an F(2)GL(r, 2)-module. It is observed that the variety of all 4-Engel groups of exponent 4 is insoluble, but not minimal insoluble.

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Original languageEnglish
Pages (from-to)747-756
Number of pages10
JournalJournal of the London Mathematical Society
Volume60
Publication statusPublished - Dec 1999

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