In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.

This paper proposes a new neocognitron that accepts incremental learning, without giving a severe damage to old memories or reducing learning speed. The new neocognitron uses a competitive learning, and the learning of all stages of the hierarchical network progresses simultaneously. To increase the learning speed, conventional neocognitrons of recent versions sacrificed the ability of incremen...