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Transactions of the American Mathematical Society

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Spherical space forms revisited


Author: Daniel Allcock
Journal: Trans. Amer. Math. Soc. 370 (2018), 5561-5582
MSC (2010): Primary 20B10; Secondary 57S17, 57S25
DOI: https://doi.org/10.1090/tran/7167
Published electronically: April 25, 2018
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Abstract: We give a simplified proof of J. A. Wolf's classification of finite groups that can act freely and isometrically on a round sphere of some dimension. We slightly improve the classification by removing some nonobvious redundancy. The groups are the same as the Frobenius complements of finite group theory.


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Additional Information

Daniel Allcock
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1202
Email: allcock@math.utexas.edu

DOI: https://doi.org/10.1090/tran/7167
Keywords: Spherical space form, Frobenius complement
Received by editor(s): March 3, 2016
Received by editor(s) in revised form: September 13, 2016, and December 8, 2016
Published electronically: April 25, 2018
Additional Notes: This work was supported by NSF grant DMS-1101566
Article copyright: © Copyright 2018 American Mathematical Society

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