Abstract. In this paper, we study single-variable linear functional equations that involve one unknown function and a finite set of known functions forming a group under composition. The main results present the complete description of the solution set, and provide an alternative and effective approach for some known facts. In the proofs, the standard methods of Linear Algebra, of Group Theory, and the Axiom of Choice play a key role.

DOI: 10.14232/actasm-016-526-9

AMS Subject Classification (1991): 39B22, 15A03, 15A06, 20F38

Keyword(s): functional equations of a single variable, rank of matrices, permutations of matrices, finite groups, cosets of finite groups

Received April 19, 2016, and in revised form July 21, 2016. (Registered under 26/2016.)