Blocks of Finite Groups pp 193-207 | Cite as

# On the Exponential and Logarithmic Functions in O-algebras

Chapter

## Abstract

Here, we assume that the quotient field *K* of O has characteristic zero. If O contains a primitive *p*-th root of unity ξ then, in suitable ideals of the commutative O-algebras, we can consider the so-called *exponential function*. As usual, this function is a homomorphism from the additive structure to the multiplicative one; in particular, the multiplication by *n* ∈ ℕ becomes the *n*-th power, and thus this function is helpful in proving the existence of the *n*-th root of some elements. In §14 and §15, we need this kind of results; in this section, we will prove them.

## Keywords

Exponential Function Power Function Finite Group Characteristic Zero Logarithmic Function
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## Copyright information

© Springer-Verlag Berlin Heidelberg 2002