  We revise existing group-theoretical approaches for a treatment of
nonrelativistic collinear magnetic systems with perfect translation invariance.
We show that full symmetry groups of these systems, which contain elements with
independent rotations in the spin and configuration spaces (spin groups), can
be replaced by magnetic groups consisting of elements with rotations acting
only on position vectors. This reduction follows from modified transformation
properties of electron spin, which in the considered systems becomes
effectively a pseudoscalar quantity remaining unchanged upon spatial operations
but changing its sign due to an operation of antisymmetry. We introduce a
unitary representation of the relevant magnetic point groups and use it for a
classification of collinear magnets from the viewpoint of
antiferromagnetism-induced spin splitting of electron bands near the center of
Brillouin zone. We prove that the recently revealed different altermagnetic
classes correspond in a unique way to all nontrivial magnetic Laue classes,
i.e., to the Laue groups containing the operation of antisymmetry only in
combination with a spatial rotation. Four of these Laue classes are found
compatible with a nonzero spin conductivity. Subsequent inspection of a simple
model allows us to address briefly the physical mechanisms responsible for the
spin splitting in real systems.
