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On orders solely of abelian groups

Published online by Cambridge University Press:  18 May 2009

S. Srinivasan
S. Srinivasan
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India
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Let n = be the factorization of an integer n(>1) into prime powers, and set Φ(n):= . In particular, for squarefree n, Φ(n) = phi;(n). Consider the set

.

It is known (from [5]) that A consists precisely of those integers n for which there is no non-abelian group of order n. It is also known (from [7]) that the set

consists solely of integers n with the property that every group of order n is cyclic. We set C′ = A – C.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 105 - 108
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

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