ON MINIMAL ORDERS OF GROUPS WITH ODD ORDER AUTOMORPHISM GROUPS

被引：0

作者：

Curran, M. John ^{[1
]}

Higgs, Russell J. ^{[2
]}

机构：

[1] Univ Otago, Dept Math & Stat, Dunedin 9054, New Zealand

[2] Univ Coll Dublin, Sch Math Sci, Dublin 2, Ireland

来源：

COMMUNICATIONS IN ALGEBRA | 2011年 / 39卷 / 01期

关键词：

Automorphism group; NI group;

D O I：

10.1080/00927870903454557

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group. Suppose that the number of prime factors of the order of G, counting repetitions, is less than or equal to five and that the order of G is not equal to p(5) for some prime number p > 3. Then we show that the order of the automorphism group of G is even. We finish with some conjectures on the smallest groups with certain odd order automorphism groups.

引用

页码：199 / 208

页数：10

共 50 条

[1] Minimal odd order automorphism groups
Hegarty, Peter
MacHale, Desmond
JOURNAL OF GROUP THEORY, 2010, 13 (02) : 243 - 255
[2] P-GROUPS WITH ODD ORDER AUTOMORPHISM GROUPS
HEINEKEN, H
LIEBECK, H
ARCHIV DER MATHEMATIK, 1973, 24 (05) : 465 - 471
[3] Finite groups with a splitting automorphism of odd order
Kıvanç Ersoy
Archiv der Mathematik, 2016, 106 : 401 - 407
[4] Finite groups with a splitting automorphism of odd order
Ersoy, Kivanc
ARCHIV DER MATHEMATIK, 2016, 106 (05) : 401 - 407
[5] On the orders of automorphism groups of finite groups
Bray, JN
Wilson, RA
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2005, 37 : 381 - 385
[6] Sums of element orders in groups of odd order
Herzog, Marcel
Longobardi, Patrizia
Maj, Mercede
INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 2021, 31 (06) : 1049 - 1063
[7] ODD ORDER GROUPS WITH AN AUTOMORPHISM CUBING MANY ELEMENTS
DEACONESCU, M
MACHALE, D
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1989, 46 : 281 - 288
[8] Minimal Abelian groups that are not automorphism groups
Ban, GN
Yu, SX
ARCHIV DER MATHEMATIK, 1998, 70 (06) : 427 - 434
[9] Minimal Abelian groups that are not automorphism groups
Guining Ban
Shuxia Yu
Archiv der Mathematik, 1998, 70 : 427 - 434
[10] AUTOMORPHISM GROUPS OF PARTIAL ORDERS
BIRD, EH
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (05) : 1011 - 1015

← 1 2 3 4 5 →