# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 36 (2007) pp.121-127

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### Abstract

Let $G$ is a group. In the case where $G$ is finite, Oliver-Petrie defined a Burnside module $\Omega(G, {\cal F})$ consisting of all equivalent classes of $\cal F$-complex. The purpose of this paper is to define the universal Burnside module $U(G, {\cal F})$. If $G$ is finite, we have $U(G, {\cal F}) \cong \Omega(G, {\cal F})$.

MSC(Primary) 57S15 57S25 $G$-$CW$-complex, $\cal F$-complex, Universal Burnside module.