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For $G$ a finite group, its Artin-Lam induction exponent is the minimum $e(G)$ among positive natural numbers such that the $e(G)$-dimensional trivial representation is in the ideal of the rational representation ring of $G$ which is generated by $G$-representations that are induced by cyclic subgroups of $G$.
This definition according to the abstract of Madsen, Thomas & Wall 1983. Other authors take the smallest $e(G)$ such that $e(G) \cdot \chi$ is in this ideal for all rational representations $\chi$ (e.g. Yamauchi 70), in which case $e(G)$ is the exponent of the additive group underlying the quotient by the ideal, whence the terminology.
The original article:
Further discussion:
Kenichi Yamauchi, On the 2-part of Artin Exponent of Finite Groups, Science Reports of the Tokyo Kyoiku Daigaku, Section A Vol. 10, No. 263/274 (1970), 234-240 (jstor:43698746)
K. K. Nwabueze, Some definition of the Artin exponent of finite groups (arXiv:math/9611212)
S. Jafari and H. Sharifi, On the Artin exponent of some rational groups, Communications in Algebra, 46:4, 1519-152 (doi:10.1080/00927872.2017.1347665)
Textbook account:
Application to discussion of free group actions on n-spheres:
Last revised on October 27, 2021 at 18:30:34. See the history of this page for a list of all contributions to it.