A NOTE ON RHODES AND GOTTLIEB-RHODES GROUPS

作者：Choi Kyoung Hwan^*; Jo Jang Hyun^*; Moon Jae Min^*

来源：Tohoku Mathematical Journal, 2016, 68(1): 139-159.

DOI：10.2748/tmj/1458248865

• Fox homotopy group
• Gottlieb group
• Gottlieb-Fox group
• Gottlieb-Rhodes group
• Rhodes group

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.

• 出版日期2016-3