A Heuristic Algorithm on Solving the Great Group Dividing of Figure

The problem of the great group of a figure is the famous NP-difficult problem. There exists an algorithm of solving the great group of figure or only applying to some of the special figure .There need time price is index level, and is low efficiency. It puts forward a kind of solving the minimax group partition algorithm with the most magnanimous nodes for elicitation information. This algorithm can be applied to any simple figure, and the maximum time complexity of algorithm is O(sn3).

Groups with a nilpotent triple factorisation

In the investigation of factorised groups one often encounters groups G = AB = AK = BK which have a triple factorisation as a product of two subgroups A and B and a normal subgroup K of G. It is of particular interest to know whether G satisfies some nilpotency requirement whenever the three subgroups A, B and K satisfy this same nilpotency requirement. A positive answer to this problem for the classes of nilpotent, hypercentral and locally nilpotent groups is given under the hypothesis that K is a minimax group or G has finite abelian section rank. The results become false if K has only finite Prüfer rank. Some applications of the main theorems are pointed out.