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    SCOPUS SCIE

    A note on Rhodes and Gottlieb-Rhodes groups

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    https://www.riss.kr/link?id=A107710884

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    <P>The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based G-space (X, x(0), G) with free and properly discontinuous G-action, if (X, x(0), G) is homotopically n-equivariant, then the n-th Gottlieb-Rhodes group G sigma(n) (X, x(0), G) is isomorphic to the n-th Gottlieb-Fox group G tau(n) (X/G, p(x(0))). Secondly, we prove that every short exact sequence of groups is n-Rhodes-Fox realizable for any positive integer n. Finally, we present some positive answers to restricted realization problems for Gottlieb-Fox groups and Gottlieb-Rhodes groups.</P>
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    <P>The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based G-space (X, x(0), G) with free...

    <P>The purpose of this paper is to give positive answers to some questions which are related to Fox, Rhodes, Gottlieb-Fox, and Gottlieb-Rhodes groups. Firstly, we show that for a compactly generated Hausdorff based G-space (X, x(0), G) with free and properly discontinuous G-action, if (X, x(0), G) is homotopically n-equivariant, then the n-th Gottlieb-Rhodes group G sigma(n) (X, x(0), G) is isomorphic to the n-th Gottlieb-Fox group G tau(n) (X/G, p(x(0))). Secondly, we prove that every short exact sequence of groups is n-Rhodes-Fox realizable for any positive integer n. Finally, we present some positive answers to restricted realization problems for Gottlieb-Fox groups and Gottlieb-Rhodes groups.</P>

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