Finite groups with a given absolute central factor group

被引：9

作者：

Chaboksavar, M. ^{[1
]}

Ghouchan, M. Farrokhi Derakhshandeh ^{[2
]}

Saeedi, F. ^{[1
]}

机构：

[1] Islamic Azad Univ, Mashhad Branch, Dept Math, Mashhad, Iran

[2] Ferdowsi Univ Mashhad, Dept Pure Math, Mashhad, Iran

来源：

ARCHIV DER MATHEMATIK | 2014年 / 102卷 / 05期

关键词：

Absolute central factor; Autocapable; Capable; Autocommutator; AUTOMORPHISMS; SUBGROUPS;

D O I：

10.1007/s00013-014-0640-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a group and L(G) be the absolute center of G, that is, the set of all elements of G fixed by all automorphisms of G. In this paper, we classify all finite groups G whose absolute central factors are isomorphic to a cyclic group, Z(p) x Z(p), D-8, Q(8), or a non-abelian group of order pq for some distinct primes p and q.

引用

页码：401 / 409

页数：9

共 12 条

[1] AUTOMORPHISMS OF A P-GROUP [J].

ADNEY, JE ;

YEN, T .

ILLINOIS JOURNAL OF MATHEMATICS, 1965, 9 (01) :137-&

[2] Groups with abelian central quotient group [J].

Baer, Reinhold .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1938, 44 (1-3) :357-386

[3] Automorphisms of direct products of finite groups [J].

Bidwell, J. N. S. ;

Curran, M. J. ;

McCaughan, D. J. .

ARCHIV DER MATHEMATIK, 2006, 86 (06) :481-489

[4]

Curran M. J., 2008, Math. Proc. R. Ir. Acad, V108, P205, DOI [10.3318/PRIA.2008.108.2.205, DOI 10.3318/PRIA.2008.108.2.205]

[5] On the autocommutator subgroup and absolute centre of a group [J].

Dietrich, Heiko ;

Moravec, Primoz .

JOURNAL OF ALGEBRA, 2011, 341 (01) :150-157

[6]

Hall M., 1964, The groups of order 2n (n = 6)

[7] Autocommutator subgroups of finite groups [J].

Hegarty, PV .

JOURNAL OF ALGEBRA, 1997, 190 (02) :556-562

[8] Derived subgroups and centers of capable groups [J].

Isaacs, IM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (10) :2853-2859

[9] Bounds for the index of the centre in capable groups [J].

Podoski, K ;

Szegedy, B .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 133 (12) :3441-3445

[10] On capability of finite abelian groups [J].

Sunic, Zoran .

ARCHIV DER MATHEMATIK, 2009, 93 (01) :23-28

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