Recursive sequences attached to modular representations of finite groups

The core of a finite-dimensional modular representation M finite group G is its largest non-projective summand. We prove that the dimensions cores M⊗n have algebraic Hilbert series when Omega-algebraic, in sense summands fall into finitely many orbits under action syzygy operator Ω. Similarly, we these dimension sequences are eventually linearly recursive what term Ω+-algebraic. This partially answers conjecture by Benson and Symonds. Along way, also number auxiliary permanence results for linear recurrence operations on multi-variable sequences.