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2002 Smith equivalence and finite Oliver groups with Laitinen number 0 or 1
Krzysztof Pawałowski, Ronald Solomon
Algebr. Geom. Topol. 2(2): 843-895 (2002). DOI: 10.2140/agt.2002.2.843

Abstract

In 1960, Paul A. Smith asked the following question. If a finite group G acts smoothly on a sphere with exactly two fixed points, is it true that the tangent G–modules at the two points are always isomorphic? We focus on the case G is an Oliver group and we present a classification of finite Oliver groups G with Laitinen number aG=0 or 1. Then we show that the Smith Isomorphism Question has a negative answer and aG2 for any finite Oliver group G of odd order, and for any finite Oliver group G with a cyclic quotient of order pq for two distinct odd primes p and q. We also show that with just one unknown case, this question has a negative answer for any finite nonsolvable gap group G with aG2. Moreover, we deduce that for a finite nonabelian simple group G, the answer to the Smith Isomorphism Question is affirmative if and only if aG=0 or 1.

Citation

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Krzysztof Pawałowski. Ronald Solomon. "Smith equivalence and finite Oliver groups with Laitinen number 0 or 1." Algebr. Geom. Topol. 2 (2) 843 - 895, 2002. https://doi.org/10.2140/agt.2002.2.843

Information

Received: 15 September 2001; Accepted: 17 June 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 1022.57019
MathSciNet: MR1936973
Digital Object Identifier: 10.2140/agt.2002.2.843

Subjects:
Primary: 20D05, 57S17, 57S25
Secondary: 55M35, 57R65.

Rights: Copyright © 2002 Mathematical Sciences Publishers

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