  ABSTRACT. Let $\Phi$ be a finite dimensional $K$-algebra and let $\mathscr{C}
= \textrm{mod}\: \Phi$ be the abelian category of finitely generated right
$\Phi$-modules. In their 1985 paper ``Modules determined by their composition
factors'', Auslander and Reiten showed that under certain conditions modules in
$\textrm{mod}\: \Phi$ are determined by their composition factors, and show an
important formula related to the Auslander-Reiten translation.
  Let $\mathscr{T}$ be a $d$-cluster tilting subcategory of $\mathscr{C}$,
which by definition is also $d$-abelian. In this paper we will define the
Grothendieck group for a $d$-abelian category, and show that the Grothendieck
groups of $\mathscr{C}$ and $\mathscr{T}$ are isomorphic. We show also that
under certain conditions, the indecomposable objects of $\mathscr{T}$ are
determined up to isomorphism by their composition factors in $\mathscr{C}$.
Finally, we generalise the formula from Auslander and Reiten involving the
higher dimensional Auslander-Reiten translation.
