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On Finite NDC -Groups
Bulletin of the Malaysian Mathematical Sciences Society ( IF 1.2 ) Pub Date : 2019-11-11 , DOI: 10.1007/s40840-019-00856-z
Pengfei Bai , Xiuyun Guo , K. P. Shum

A finite p-group G is called a NDC-group if \(G'/{G' \cap N}\) is cyclic or \(N/{N \cap Z(G)}\) is cyclic for every normal subgroup N in G. In this paper, first we give some properties of NDC-groups and in particular, we give the order of \(G'Z(G)/Z(G)\) for a NDC-group G so that we could investigate the structure of NDC-groups. Next, some necessary and sufficient conditions for a p-group G whose quotient group G / Z(G) is generated by two elements to be a NDC-group are given. Finally, we also give some further properties of p-groups with small derived subgroups by using the properties of capable p-groups with small generating systems, which maybe could apply some other research of p-groups.

中文翻译:

在有限NDC上

如果\(G'/ {G'\ cap N} \)是循环的或\(N / {N \ cap Z(G)} \)对于每个法线都是循环的,则一个有限的p-G称为NDC-子组ñģ。在本文中,我们首先得到的一些性质NDC -基团,特别是,我们给出的顺序\(的G'z(G)/ Z(G)\)NDC -基ģ,以便我们能够调查结构的NDC -基团。接着,对于一些充分必要条件p -基团ģ其商群G ^  /  ŽG)由两个元素生成,从而给出NDC -group。最后,我们还通过使用具有小型发电系统的有能力的p-基团的性质,给出了具有较小派生子组的p-基团的其他性质,这也许可以应用于p-基团的其他研究。
更新日期:2019-11-11
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