This paper aims at introducing an electron model derived from a theory previously developed by us for the classical electron, and then extended to the quantal case, based on the introduction of the chronon. Such a theory, besides the «macroscopical» motion of the particle, considers internal «microscopical» motions to which the «structure» of the electron is possibly related. This problem is approached with a procedure based on group theory, from which one derives that a space-time microuniverse of the De Sitter type, where the «internal motions» of the electron take place, can be associated with the electron. The intrinsic properties of the particle are originated by those motions. The description of the particle by an observer is given by means of the geodetical projection of the De Sitter space-time on a flat variety, consisting of a piece of the Minkowski space-time called Castelnuovo universe. In this variety the electron behaves as a 3-dimensional oscillating microcosmos reducing to a point at the extremes of any fundamental interval of proper time, when the macroscopical motion of the particle is defined. For such a motion, the electron can be considered as a point particle moving in the ordinary Minkowski space-time. It is also shown how the internal motion of the free electron associates to this particle of rest massm0 an intrinsic energym0c2, given by the kinetic energy of the electron itself, and an intrinsic magnetic moment µа=(1/4π)(e3/e0c2) equal to the first approximation of the anomalous magnetic moment predicted by Schwinger's quantum electrodynamics. Finally, we note that the present model of the electron affords a promising start toward the understanding of the meaning of the fine-structure constant.