Words Which Give Rise to Another Group Operation for a Given Group

Cooper, C. D. H.

doi:10.1007/978-3-662-21571-5_19

C. D. H. Cooper²

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 372))

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Abstract

For any group G, the binary operation x * y = yx is a group operation, expressed in terms of the word yx , which gives a different (unless G is abelian) but isomorphic group structure on the set G . It is natural to ask what other group structures may be defined on G by an operation of the form

$$x * y = W\left( {x,y} \right)$$

where W(x, y) is a word in x, y (we call such words group words for G) and whether it is possible for the new group (denoted by G _W) and G to be non-isomorphic. If so, it might be possible to discover facts about one group by considering the other — especially if one group is abelian and the other is not. Thoughts such as these have prompted this paper.

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Authors and Affiliations

Macquarie University, North Ryde, NSW, 2113, USA
C. D. H. Cooper

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C. D. H. Cooper
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Editors and Affiliations

Dept. of Mathematics, Institute of Advanced Studies, Australian National University, 2600, Canberra, ACT, Australia
M. F. Newman

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Cooper, C.D.H. (1974). Words Which Give Rise to Another Group Operation for a Given Group. In: Newman, M.F. (eds) Proceedings of the Second International Conference on the Theory of Groups. Lecture Notes in Mathematics, vol 372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21571-5_19

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DOI: https://doi.org/10.1007/978-3-662-21571-5_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06845-7
Online ISBN: 978-3-662-21571-5
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