  A Hom-group is the non-associative generalization of a group, whose
associativity and unitality are twisted by a compatible bijective map. In this
paper, we give some new examples of Hom-groups, and show the first and the
second isomorphism fundamental theorems of homomorphisms on Hom-groups. We also
introduce the notion of Hom-group action, and as an application, we show the
first Sylow theorem for Hom-groups along the line of group actions.
