We prove that the Scott module whose vertex is isomorphic to a direct product of generalized quaternion $2$-group and cyclic Brauer indecomposable. This result generalizes similar results which are obtained for abelian, dihedral, quaternion, semidihedral wreathed vertices.

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

We show that the homotopy type of a finite oriented Poincar\'{e} 4-complex is determined by its quadratic 2-type provided fundamental group and has dihedral Sylow 2-subgroup. By combining with results Hambleton-Kreck Bauer, this applies in case smooth 4-manifolds whose subgroup SO(3). An important class examples are elliptic surfaces group.

Abstract Zero-divisor codes are constructed using group rings where their generators zero-divisors. Generally, zero-divisor can be equivalent despite associated groups non-isomorphic, leading to the proposed conjecture “Every dihedral code has an form of cyclic code”. This paper is devoted study equivalence in $$F_2G$$ <mml:ms...