Some Applications of Metacyclic p-Groups of Nilpotency Class Two

Abdulqader Mohammed Abdullah Bin Basri ； Nor Haniza Sarmin ； Nor Muhainiah Mohd Ali ； James R. Beuerle

《Research Journal of Applied Sciences, Engineering and Technology》 4卷23期 (2012/12) Pp. 5217-5221

並列摘要

A group G is metacyclic if it contains a cyclic normal subgroup K such that G/K is also cyclic. Metacyclic p-groups classified by different authors. King classified metacyclic p-groups. Beuerle (2005) classified all finite metacyclic p-groups. A group is called capable if it is a central factor group. The purpose of this study is to compute the epicenter of finite nonabelian metacyclic p-groups of nilpotency class two, for some small order groups, using Groups, Algorithms and Programming (GAP) software. We also determine which of these groups are capable.

並列關鍵字

p-groups ； metacyclic groups ； epicenter and capable groups