A Non‐Finitely Based Variety of Centre‐by‐Abelian‐by‐Nilpotent Groups of Exponent 8 | Zendy

Krasilnikov Alexei N. | Zendy

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A Non‐Finitely Based Variety of Centre‐by‐Abelian‐by‐Nilpotent Groups of Exponent 8

Author(s) -

Krasilnikov Alexei N.

Publication year - 2003

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/s0024610703004319

Subject(s) - variety (cybernetics) , exponent , nilpotent , mathematics , abelian group , nilpotent group , pure mathematics , stallings theorem about ends of groups , abelian variety , finitely generated abelian group , discrete mathematics , statistics , philosophy , linguistics

The first example of a non‐finitely based variety of centre‐by‐abelian‐by‐nilpotent groups was found in 1995. This example has an infinite exponent but it can be seen that the method used to construct it also gives a variety that has an exponent of 128. Later it was proved that there exists a variety with similar properties but with an exponent of 32. The paper constructs a non‐finitely based variety of centre‐by‐abelian‐by‐nilpotent groups which has an exponent of 8.

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