We extend the notions of quasi-monomial groups and almost monomial groups, in framework supercharacter theories, we study their connection with Artin's conjecture regarding holomorphy Artin $L$-functions.

Two isometry groups of combinatorial codes are described: the group of automorphisms and the group of monomial automorphisms, which is the group of those automorphisms that extend to monomial maps. Unlike the case of classical linear codes, where these groups are the same, it is shown that for combinatorial codes the groups can be arbitrary different. Particularly, there exist codes with the fu...

We describe an algorithm for explicitly listing the irreducible monomial subgroups of GL(n, q) , given a suitable list of finite irreducible monomial subgroups of GL(n, C) , where n is 4 or a prime, and q is a prime power. Particular attention is paid to the case n = 4, and the algorithm is illustrated for n = 4 and q = 5. Certain primitive permutation groups can be constructed from a list of i...