Harmonic analysis on GF(pp∞): Part I

The profinite group which is the inverse limit of the inverse system comprised of the GF(ppℓ) with homomorphisms between them, is studied. It is shown that is a topological group isomorphic to Zp. The GF(pp∞) which is the direct limit of the direct system comprised of the GF(ppℓ) with appropriate homomorphisms between them, is the Pontryagin dual of . The Galois group of Frobenius automorphisms of GF(pp∞) (endowed with the Krull topology) is isomorphic to Zp. can also be viewed as a topological right GF(pp∞)-module. The work provides the foundations for harmonic analysis on GF(pp∞) (and is continued in part II).