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On single-law definitions of groups
Published online by Cambridge University Press: 17 April 2009
Abstract
It will be proved that any mononomic variety of groups can be considered as a variety of (ρ ε) or (ρ, τ) or (ν, ε)-algebras, or as a variety of n-groupoids—which satisfy a single law, where: xyρ = x.y−1 = xτ = x−1, xyν = x−1.y−1, ε is the identity, and for certain interpretations of the n-ary operation. The problem is discussed for Ω-groups, too.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 101 - 106
- Copyright
- Copyright © Australian Mathematical Society 1988
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