Abstract

Abstract: We address the conditions that an innermetacyclic pgroup is a capable group. We also acquire the necessary and sufficient conditions that an innermetacyclic group is a capable pgroup. We further construct a group H from an innermetacyclic pgroup G, which makes G isomorphic to H/Z(H).

Key words: innermetacyclic groups, capable group

CLC Number: 

• O152

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LI Zhixiu. Property of innermetacyclic capable group[J].SHANDONG SCIENCE, 2015, 28(5): 77-79.

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URL: https://www.sdkx.net/EN/10.3976/j.issn.1002-4026.2015.05.012

         https://www.sdkx.net/EN/Y2015/V28/I5/77

References

［1］BAER R.Groups with preassigned central and qentral guotient group［J］.Trans Amer Math Soc,1938,44(3):381-412. ［2］SHAHRIAR S. On normal subgroups of capable groups［J］. Arch Math,1987（48)：193-198. ［3］HERMANN H. Nilpotent groups of class two that can appear as central quotient groups［J］. Bend Sem Mat Univ Padova,1996（54): 347-352. ［4］李志秀.pn(n≤4)阶capable群［J］.数学的实践与认识, 2015，45（12）:246-251. ［5］BLACKBURN N. Generalizations of certain elementary theorems on p-groups［J］. Proc London Math Soc, 1961， 11 (3) ： 1-22. ［6］李志秀.亚循环capable p-群［J］.数学的实践与认识,2014，44（22）:232-235.

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