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Rings of small order

Published online by Cambridge University Press:  22 September 2016

Colin R. Fletcher
Colin R. Fletcher*
Affiliation:
Department of Pure Mathematics, University College of Wales, Aberystwyth SY23 3BZ
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Most students in their undergraduate careers ensure that they have many examples of groups at their finger tips. These include not only whole systems such as cyclic groups and symmetric groups but also specific examples, in particular groups of small order. These latter groups are useful for trying out new ideas as soon as they are encountered, such as the bogeys of cosets, normal subgroups and factor groups. If we consider only groups of order 7 or less, then we already are furnished with nine examples of cyclic, non-cyclic, abelian and non-abelian groups.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 64 , Issue 427 , March 1980 , pp. 9 - 22
Copyright
Copyright © Mathematical Association 1980

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References

1. Waterhouse, W. C., Rings with cyclic additive group, Am. Math. Monthly, 71, 449–450 (1964).Google Scholar
2. Erickson, D. B., Orders for finite non-commutative rings, Am. Math. Monthly, 73, 376–377 (1966).Google Scholar
3. Fletcher, Colin R., The structure of unique factorisation rings, Proc. Cambridge Philos. Soc. 67, 535–540 (1970).Google Scholar
4. Zariski, O. and Samuel, P., Commutative algebra, Vol. 1.Princeton University Press (1958).Google Scholar
5. Fletcher, Colin R., Euclidean rings, J. London Math. Soc. 4, 79–82 (1971).Google Scholar
6. Fletcher, Colin R. and Lidster, M., Constructing a ring without unique factorisation, Mathl Gaz. 62, 104–109 (No. 420, June 1978).Google Scholar