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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.