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On single-law definitions of groups

Published online by Cambridge University Press:  17 April 2009

Vladimir Tasić
Vladimir Tasić
Affiliation:
Balzakova 27, 21000 Novi Sad, Yugoslavia
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Abstract

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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

References

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