## Group actions on spheres with rank one isotropy

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- by Ian Hambleton and Ergün Yalçın PDF
- Trans. Amer. Math. Soc.
**368**(2016), 5951-5977 Request permission

## Abstract:

Let $G$ be a rank two finite group, and let $\mathcal {H}$ denote the family of all rank one $p$-subgroups of $G$ for which $\operatorname {rank}_p(G)=2$. We show that a rank two finite group $G$ which satisfies certain explicit group-theoretic conditions admits a finite $G$-CW-complex $X\simeq S^n$ with isotropy in $\mathcal {H}$, whose fixed sets are homotopy spheres. Our construction provides an infinite family of new non-linear $G$-CW-complex examples.## References

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## Additional Information

**Ian Hambleton**- Affiliation: Department of Mathematics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
- MR Author ID: 80380
- Email: hambleton@mcmaster.ca
**Ergün Yalçın**- Affiliation: Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey
- Email: yalcine@fen.bilkent.edu.tr
- Received by editor(s): April 9, 2014
- Received by editor(s) in revised form: September 17, 2014, and December 14, 2014
- Published electronically: October 20, 2015
- Additional Notes: This research was partially supported by NSERC Discovery Grant A4000. The second author was partially supported by TÜBİTAK-TBAG/110T712.
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 5951-5977 - MSC (2010): Primary 20J05, 55U15, 57S17, 18Gxx
- DOI: https://doi.org/10.1090/tran/6567
- MathSciNet review: 3458403