This article is cited in 1 paper

Periodic $\lambda$-rings and exponents of finite groups

A. A. Davydov

M. V. Lomonosov Moscow State University

Abstract: 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.

UDC: 512.737

MSC: 19A31, 20C15

Received: 05.11.1996

DOI: 10.4213/sm244

 English version: Sbornik: Mathematics, 1997, 188:8, 1183–1190

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