5th International Conference Noncommutative Rings and their Applications, Lens, France, 12 - 15 June 2017, vol.727, pp.25-38
We present some results related to G-groups and their category G-Grp in connection with the category Grp of all groups and the category R-Mod of all left modules over a fixed ring R. In particular, we prove that the Krull-Schmidt-Remak-Azumaya Theorem holds for G-groups, where G is a fixed group, for finite families of G-groups. A key role in this setting is played by the class of completely indecomposable G-groups.