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Multiplication on Spaces with Comultiplication*

Published online by Cambridge University Press:  20 November 2018

C.S. Hoo
C.S. Hoo*
Affiliation:
University of Alberta, Edmonton
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Let A be an H-space and K a space. It is well known that [K, A] is a loop. Suppose A has a comultiplication as well, that is, cat A < 2. Then we shall prove that [K, A] is a Moufang loop. This generalises a result of C. W. Norman who proved this for the case where A is the circle, the 3-sphere or the 7-sphere. It also improves the known result that [K, A] is a diassociative loop if A has a comultiplication as well, since Moufang loops are diassociative.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 4 , August 1969 , pp. 499 - 505
Copyright
Copyright © Canadian Mathematical Society 1969

Footnotes

*

This research was supported by NRC Grant A-3026.

References

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