Varieties of Groups of Exponent 4 | Zendy

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Varieties of Groups of Exponent 4

Author(s) -

Quick Martyn

Publication year - 1999

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610799008169

Subject(s) - subvariety , exponent , mathematics , variety (cybernetics) , group (periodic table) , pure mathematics , generator (circuit theory) , combinatorics , power (physics) , statistics , physics , thermodynamics , linguistics , philosophy , quantum mechanics

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 ⩾ 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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