Extension of Maschke’s theorem

Abstract

© 2019, © 2019 Taylor & Francis Group, LLC. In the present article, we examine linear representations of finite gyrogroups, following their group-counterparts. In particular, we prove Maschke’s theorem for gyrogroups, along with its converse. This suggests studying the left regular action of a gyrogroup (G,⊕) on the function space (Formula presented.) in a natural way, where L(G) is the space of all functions from G to a field.