Elementary definition of n-groups without higher category or homotopy theory

Develop an elementary definition of n-groups (higher groups) that does not rely on higher category theory or homotopy theory, to provide an accessible framework compatible with the combinatorial and algebraic approach of groupspaces.

Background

In discussing potential connections between groupspaces and n-groups, the author reports an inability to find an elementary definition of n-groups that avoids advanced machinery from higher category or homotopy theory.

Providing such a definition would make n-groups more accessible to researchers working within the groupspace framework and could facilitate a direct comparison or integration of the two theories.