ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS

被引：17

作者：

Jamali, A. R. ^{[1
]}

Viseh, M. ^{[1
]}

机构：

[1] Tarbiat Moallem Univ, Fac Math Sci & Comp, Tehran 15618, Iran

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2013年 / 87卷 / 02期

关键词：

finite p-groups; noninner automorphism; powerful p-groups; cyclic commutator subgroup; P-GROUPS;

D O I：

10.1017/S0004972712000706

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Phi(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.

引用

页码：278 / 287

页数：10

共 13 条

[1] Finite p-groups of class 2 have noninner automorphisms of order p [J].

Abdollahi, A. .

JOURNAL OF ALGEBRA, 2007, 312 (02) :876-879

[2] Powerful p-groups have non-inner automorphisms of order p and some cohomology [J].

Abdollahi, Alireza .

JOURNAL OF ALGEBRA, 2010, 323 (03) :779-789

[3]

Berkovich Y, 2008, DEGRUYTER EXPOS MATH, V46, P1, DOI 10.1515/9783110208221

[4] ENDOMORPHISMS OF 2-GENERATED METABELIAN-GROUPS THAT INDUCE THE IDENTITY MODULO THE DERIVED SUBGROUP [J].

CARANTI, A ;

SCOPPOLA, CM .

ARCHIV DER MATHEMATIK, 1991, 56 (03) :218-227

[5] ON FINITE P-GROUPS WITH CYCLIC COMMUTATOR SUBGROUP [J].

CHENG, Y .

ARCHIV DER MATHEMATIK, 1982, 39 (04) :295-298

[6] Noninner automorphisms of order p of finite p-groups [J].

Deaconescu, M ;

Silberberg, G .

JOURNAL OF ALGEBRA, 2002, 250 (01) :283-287

[7]

Finogenov A., 1995, ALGEBR LOG+, V34, P125

[8] NICHTABELSCHE P-GRUPPEN BESITZEN AUSSERE P-AUTOMORPHISMEN [J].

GASCHUTZ, W .

JOURNAL OF ALGEBRA, 1966, 4 (01) :1-&

[9]

KURZWEIL H, 2004, UNIVERSITEX, P64, DOI 10.1007/b97433

[10]

LIEBECK H, 1965, J LONDON MATH SOC, V40, P268

← 1 2 →