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Groups in modular arithmetic

Published online by Cambridge University Press:  22 September 2016

K. Robin McLean
K. Robin McLean*
Affiliation:
School of Education, 19-23 Abercromby Square, P.O. Box 147, Liverpool L69 3BX
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Extract

It has often been noted that modular arithmetic provides a rich source of supply of groups. Indeed, a remarkable theorem asserts that any finite commutative group can be found by a sufficiently diligent search through the multiplicative groups and subgroups of modular arithmetic! During the last few years two articles in this area have appeared in Mathematics Teaching. In the first [1], Tim Brand drew attention to the fact that such a multiplicative group can have an identity element other than 1. (For example, 8 is the identity of the group {2,4,8} under multiplication mod 14.) More recently [2] Geoff Saltmarsh described an ingenious way of finding the identity and put forward an interesting conjecture about these groups.

Type
Research Article
Information
The Mathematical Gazette , Volume 62 , Issue 420 , June 1978 , pp. 94 - 104
Copyright
Copyright © Mathematical Association 1978 

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References

1. Brand, T. E., Some surprising identity elements, Maths Teaching 64, 50–52 (September 1973).Google Scholar
2. Saltmarsh, G. S., Identity elements, Maths Teaching 79, 33 (June 1977).Google Scholar
3. Davenport, H., The higher arithmetic. Hutchinson (1952).Google Scholar