  We use the gluing construction introduced by Jia Huang to explore the rings
of invariants for a range of modular representations. We construct generating
sets for the rings of invariants of the maximal parabolic subgroups of a finite
symplectic group and their common Sylow $p$-subgroup. We also investigate the
invariants of singular finite classical groups. We introduce parabolic gluing
and use this construction to compute the invariant field of fractions for a
range of representations. We use thin gluing to construct faithful
representations of semidirect products and to determine the minimum dimension
of a faithful representation of the semidirect product of a cyclic $p$-group
acting on an elementary abelian $p$-group.

Commutative Algebra;Representation Theory