## Osaka Journal of Mathematics

### The converse of isovariant Borsuk-Ulam results for some abelian groups

Ikumitsu Nagasaki

#### Abstract

The isovariant Borsuk-Ulam theorem provides nonexistence results on isovariant maps between representations. In this paper we shall deal with the existence problem of isovariant maps as a converse to the isovariant Borsuk-Ulam theorem, and show that the converse holds for representations of an abelian $p$-group or a cyclic groups of order $p^{n}q^{m}$ or $pqr$, where $p,q,r$ are distinct primes.

#### Article information

Source
Osaka J. Math., Volume 43, Number 3 (2006), 689-710.

Dates
First available in Project Euclid: 25 September 2006

https://projecteuclid.org/euclid.ojm/1159190009

Mathematical Reviews number (MathSciNet)
MR2283417

Zentralblatt MATH identifier
1157.57023

Subjects
Primary: 57S17: Finite transformation groups

#### Citation

Nagasaki, Ikumitsu. The converse of isovariant Borsuk-Ulam results for some abelian groups. Osaka J. Math. 43 (2006), no. 3, 689--710. https://projecteuclid.org/euclid.ojm/1159190009

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