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数学进展 - 2018, Vol. 47(2): 215-223
研究论文
型不变量为 $(e_1, e_2, 1)$的正则$p$群的分类
A Classification of Regular $p$-groups with Type $(e_1, e_2, 1)$

宋蔷薇1,张丽华2
SONG Qiangwei1,*, ZHANG Lihua2

1. 山西师范大学数学与计算机科学学院, 临汾, 山西, 041004;
2. 北京邮电大学数学系, 北京, 100876
1. School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, 041004, P. R. China;
2. Department of Mathematics, Beijing University of Posts and Telecommunications, Beijing, 100876, P. R. China

收稿日期: 2016-06-24
出版日期: 2018-05-16
2018, Vol. 47(2): 215-223
DOI: 10.11845/sxjz.2016085b


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摘要 本文给出了型不变量为$(e_1, e_2, 1)$的正则$p$群的分类, 其中$e_1\geq 2e_2$, $e_2\geq 3$.
关键词 有限$p$群正则$p$群亚交换$p$群$p$交换$p$群    
Abstract:The regular $p$-groups with Type $(e_1, e_2, 1)$ are classified up to isomorphism, where $e_1\geq 2e_2$ and $e_2\geq 3$.
Key wordsfinite $p$-groups    regular $p$-groups    metabelian $p$-groups    $p$-abelian $p$-groups
PACS:  O152.1  
[1] Hall, P., A contribution to the theory of groups of prime-power order, Proc. Lond. Math. Soc. (2), 1934, 36: 29-95.
[2] Hua, L.K. and Tuan, H.F., Determination of the groups of odd-prime-power order $p^n$ which contain a cyclic subgroup of index $p^2$, Sci. Rep. Nat. Tsing Hua Univ. (A), 1940, 4: 145-154.
[3] Ji, Y.H., Du, S.F. and Zhang, L.L., A classification of regular $p$-groups with invariants $(e,2,1)$, Southeast Asian Bull. Math., 2001, 25: 245-256.
[4] Robinson, D.J.S., A Course in the Theory of Groups, Second Edition, New York: Springer-Verlag, 1996.
[5] Xu, M.Y., A complete classification of metacyclic $p$-groups of odd order, Adv. Math. (China), 1983, 12(1): 72-73 (in Chinese).
[6] Xu, M.Y., A theorem on metabelian $p$-groups and some consequences, Chin. Ann. Math. Ser. B, 1984, 5(1): 1-6.
[7] Xu, M.Y., The power structure of finite $p$-groups, Bull. Aust. Math. Soc., 1987, 36(1): 1-10.
[8] Xu, M.Y., P. Hall's basis theorem for regular $p$-groups and its application to some classification problems, Comm. Algebra, 1991, 19(4): 1271-1280.
[9] Xu, M.Y. and Qu, H.P., Finite $p$-groups, Beijing: Peking Univ. Press, 2010 (in Chinese).
[10] Xu, M.Y. and Zhang, Q.H., A classification of metacyclic $2$-groups,Algebra Colloq., 2006, 13(1): 25-34.
[11] Zhang, Q.H. and Li, P.J., Finite $p$-groups with a cyclic subgroup of index $p^3$, J. Math. Res. Appl., 2012, 32(5): 505-529.
[12] Zhang, Q.H., Song, Q.W. and Xu, M.Y., A classification of some regular $p$-groups and its applications, Sci. Sin. Math.,2006, 49(3): 366-386 (in Chinese).
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