The authors discuss whole-number representations to a symmetrica! group of the third degree. It is shown that there exists only a finite number, i. e. ten, prime representations of this group. The dimensions of the prime representations do not exceed the order of the group.
It is further shown that the factoring of any representation into a direct sum of primes is univalent.
Thus the first example has been given of a complete description of whole-number representations of a non-commutative group.
Citation Example:Nazarova L. A., Roiter A. V. Whole-number representations of a symmetrical
group of third degree // Ukr. Mat. Zh. - 1962. - 14, № 3. - pp. 271-288.