Bounds for the number of automorphisms of a compact non-orientable surface

The paper shows that for every positive integer p > 2, there exists a compact non-orientable surface of genus p with at least 4p automorphisms if p is odd, or at least 8 (p - 2) automorphisms if p is even, with improvements for odd p ≢ 3 mod 12. Further, these bounds are shown to be sharp (in that no larger group of automorphisms exists with genus p) for infinitely many values of p in each congruence class modulo 12, with the possible (but unlikely) exception of 3 mod 12.