Orbits of the Automorphism Group of a Module over a Principal Ideal Ring / A. A. Garazha. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2016. № 5. P. 37-40 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 196-199].

Orbits of the automorphism group of a finitely generated module over a principal ideal ring are described in terms of canonical representatives and by a complete system of invariants. For a primary module, a natural bijection to a sum of two Young diagrams is established for the set of orbits and the set of partitions of the Young diagram corresponding to the module, which allows us to calculate the number of orbits.

Key words: automorphism group, orbit, module over a principal ideal domain, Young diagram.

№ 5/2016