The Orders of the Automorphism Groups of all Groups of Order p5

Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (4): 495-503.

The Orders of the Automorphism Groups of all Groups of Order p⁵

1. College of Mathematics and Computer Science, Guangxi University for Nationalities 2. College of Mathematics and Information Science, Guangxi University

Received:2011-01-19 Online:2012-12-30 Published:2023-03-15
About author:LAN Yong-hong(1968-), male, native of Nanning, Guangxi, a lecturer of Guangxi University for Nationalities, M.S.D., engages in finite group; HUI Min(1987-), female, native of Baoji, Shaanxi, M.S.D., engages in finite group; BAN Gui-ning(1962-), male, native of Nanning, Guangxi, a professor of Guangxi University, Ph.D., engages in finite group and control theory; SHAO Ming-wen(1969-), male, native of Jinan, Shandong, Ph.D., engages in finite group.
Supported by:
Supported by the National Natural Science Foundation of China(61074185);Supported by the Projection of Science and Technique for Guangdong Province(2009B030802044);Supported by the Projection of Production, Study and Investigation for Guangdong Province(2010B090301042);Supported by the Science and Study Foundation of Guangxi University(XB2100285)

Abstract

Abstract: In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field, completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall’s concept of isoclinism, also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.

Key words: finite group, p-group, automorphism, field, finite field

CLC Number:

O151.21

LAN Yong-hong, HUI Min, BAN Gui-ning, SHAO Ming-wen. The Orders of the Automorphism Groups of all Groups of Order p⁵[J]. Chinese Quarterly Journal of Mathematics, 2012, 27(4): 495-503.

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The Orders of the Automorphism Groups of all Groups of Order p⁵

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