  An algebraic description of basic discrete symmetries (space inversion P,
time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT)
is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of
multidimensional spaces over the fields of real and complex numbers are
considered in terms of fundamental automorphisms of Clifford algebras. The
fundamental automorphisms form a finite group of order 4. The charge
conjugation is represented by a pseudoautomorphism of the Clifford algebra.
Such a description allows one to extend the automorphism group. It is shown
that an extended automorphism group (CPT-group) forms a finite group of order
8. The group structure and isomorphisms between the extended automorphism
groups and finite groups are studied in detail. It is proved that there exist
64 different realizations of CPT-group. An extension of universal coverings
(Clifford-Lipschitz groups) of the orthogonal groups is given in terms of
CPT-structures which include well-known Shirokov-Dabrowski PT-structures as a
particular case.
