Geodesic
Periodic $\lambda$-rings and exponents of finite groups
Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1183-1190 Cet article a éte moissonné depuis la source Math-Net.Ru

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A $\lambda$-ring is said to be $n$-periodic if its Adams operators satisfy the relation $\psi^{i+n}=\psi^i$ for each $i$. The quotient by the radical of the free periodic $\lambda$-ring generated by one element is described. Using this description, the order of a finite group is shown to divide the group's exponent to the power equal to the dimension of an arbitrary faithful complex representation. 
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     title = {Periodic $\lambda$-rings and exponents of finite groups},
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A. A. Davydov. Periodic $\lambda$-rings and exponents of finite groups. Sbornik. Mathematics, Tome 188 (1997) no. 8, pp. 1183-1190. http://geodesic.mathdoc.fr/item/SM_1997_188_8_a4/

[1] Molien T., “Über die Invarianten der linear Substitutionsgruppen”, Sitzungsber. König. Preuss. Akad. Wiss., 1897, 1152–1156 | Zbl

[2] Grothendieck A., Special $\lambda$-rings, rukopis | Zbl

[3] Adams J. F., “Vector fields on spheres”, Ann. of Math., 75 (1962), 603–632 | DOI | MR | Zbl

[4] Atiyah M. F., Tall D. O., “Group representations, $\lambda$-rings and $J$-homomorphism”, Topology, 8:3 (1963), 253–297 | DOI | MR

[5] Kervair M., “Opération d'Adams en théorie des représentations linéares des groupes finis”, Enseign. Math. Ser. 2, 22:1 (1976), 1–28 | MR | Zbl

[6] Knutson D., $\lambda$-rings and the representation theory of the symmetric group, Lecture Notes in Math., 308, Springer-Verlag, Berlin, 1973 | MR | Zbl