JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2020, Vol. 55 ›› Issue (8): 92-97.doi: 10.6040/j.issn.1671-9352.0.2019.438

Previous Articles    

A classs of finite p-groups with few normal subgroups

WANG Jun-xin*, BAI Peng-fei   

  1. Faculty of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Published:2020-07-14

PDF (PC)

360

Abstract: The N1-p-groups are completely classified. The so-called N1-group is a group G that has only one normal subgroup which neither contains G' nor is contained in Z(G).

Key words: N1-p-group, derived subgroup G', center Z(G)

CLC Number: 

  • O152.1
[1] DEDEKIND R. Über gruppen, deren samtliche Teiler normalteiler sind[J]. Math Ann, 1897, 48:548-561.
[2] AN Lijian, ZHANG Qinhai. Finite metahamiltonian p-groups[J]. J Algebra, 2015, 442:23-35.
[3] PASSMAN D S. Nonnormal subgroups of p-groups[J]. J Algebra, 1970, 15:352-370.
[4] ZHANG Qinhai, GUO Xiaoqiang, QU Haipeng, et al. Finite groups which have many normal subgroups[J]. J Korean Math Soc, 2009, 46:1165-1178.
[5] SILBERBERG G. Finite p-groups with few normal subgroups[J]. Bull Belg Math Soc, 2000, 7:365-376.
[6] SILBERBERG G. Finite p-groups with few normal subgroups(Ⅱ)[J]. Bull Belg Math Soc, 2002, 9:185-192.
[7] BAI Pengfei, GUO Xiuyun. On finite p-groups with few normal subgroups[J]. J Algebra and Its Applications, 2017, 16, 1750159.
[8] HUPPERT B. Endliche gruppen Ⅰ [M]. Berlin: Springer, 1967.
[9] BLACKBURN N. Generalizations of certain elementary theorems on p-groups[J]. Proc London Math Soc, 1961, 11:142-143.
[10] ZHANG Qinhai, ZHAO Libo, LI Miaomiao, et al. Finite p-groups all of whose subgroups of index p3 are abelian[J]. Commun Math Stat, 2015, 3:69-162.
[11] BERKOVICH Y. Groups of prime power order Ⅰ[M]. New York: Walter de Gruyter, 2008.
[12] 徐明曜, 曲海鹏. 有限p群[M]. 北京: 北京大学出版社, 2010. XU Mingyao, QU Haipeng. Finite p-groups[M]. Beijing: Beijing University Press, 2010.
[13] 张勤海, 安立坚. 有限p群构造:下册[M]. 北京: 科学出版社, 2017. ZHANG Qinhai, AN Lijian. The structures of finite p-groups(last of two Volumes)[M]. Beijing: Science Press, 2017.
[1] CHEN Song-liang. On the structures of groups of order p2q3 with non-Abelian Sylow subgroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(12): 93-97.
[2] LI Zheng-xing, YANG Shu-xian. Note on integral group rings of holomorphs of finite metacyclic 2-groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 40-42.
[3] GAO Hui, GAO Sheng-zhe, YIN Li. On the s-θ-completions for subgroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 43-46.
[4] HAI Jin-ke, WANG Sheng-fang, LI Zheng-xing. On the maximal π-factorable subnormal pairs [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 1-3.
[5] WANG Dun-Xin. Some conditions for finite groups to be solvable [J]. J4, 2009, 44(8): 35-38.
[6] REN Xiao-qian, XU Yong-jun. PBW-deformations of type B2 quantum group and their symmetry property [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(8): 65-74.
[7] CHEN Chen, GAO Ying-ying, CHEN Hui-xiang. Lazy 2-cocycles on 9-dimensional Taft algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 73-78.
[8] LI Ning-ying, GUO Ji-dong, HAI Jin-ke. Number of homomorphisms between groups with Abel direct factors and finite groups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 59-62.
[9] DONG Shen-juan, LI Zheng-xing. On p-central automorphisms of critical groups and applications [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(2): 68-72.
[10] ZHAO Yan-wei, HAI Jin-ke. T.Asai and T.Yoshida problem of group homomorphism [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 101-105.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd