On elements of prime-power index in finite groups

被引：7

作者：

Camina, Alan R. ^{[2
]}

Shumyatsky, Pavel ^{[1
]}

Sica, Carmela ^{[3
]}

机构：

[1] Univ Brasilia, Dept Math, BR-70919 Brasilia, DF, Brazil

[2] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

[3] Univ Salerno, Dipartimento Matemat & Informat, I-84084 Fisciano, SA, Italy

来源：

JOURNAL OF ALGEBRA | 2010年 / 323卷 / 02期

关键词：

Finite groups; Centralizers;

D O I：

10.1016/j.jalgebra.2009.09.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an element x of a finite group G let Ind(G)(x) denote the index of C-G(x) in G. We prove that if Ind((a,b,x)) (x) is a prime-power for any a, b is an element of G. then Ind(G)(x) is a prime-power. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：522 / 525

页数：4

共 50 条

[21] Descriptions of groups of prime-power order
Newman, MF
Nickel, W
Niemeyer, AC
JOURNAL OF SYMBOLIC COMPUTATION, 1998, 25 (05) : 665 - 682
[22] Enumeration of groups of prime-power order
Witty, Brett E.
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2007, 76 (03) : 479 - 480
[23] ON METABELIAN GROUPS OF PRIME-POWER EXPONENT
GUPTA, ND
NEWMAN, MF
TOBIN, SJ
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1968, 302 (1469): : 237 - &
[24] Descriptions of Groups of Prime-power Order
J Symb Comput, 5 (665):
[25] Metacyclic Groups of Prime-Power Order
M.F.Newman
徐明曜
数学进展, 1988, (01) : 106 - 107
[26] Some properties of prime-power groups
Weisner, Louis
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1935, 38 (1-3) : 485 - 492
[27] The prime-power hypothesis and solvable groups
Ni Du
Mark L. Lewis
Archiv der Mathematik, 2017, 109 : 301 - 303
[28] CLASS OF GROUPS OF PRIME-POWER ORDER
WAMSLEY, JW
ISRAEL JOURNAL OF MATHEMATICS, 1972, 11 (03) : 297 - &
[29] A DATABASE OF GROUPS OF PRIME-POWER ORDER
BUTLER, G
IYER, SS
OBRIEN, EA
SOFTWARE-PRACTICE & EXPERIENCE, 1994, 24 (10): : 911 - 951
[30] On finite groups with prime-power order S-quasinormally embedded subgroups
Xianbiao Wei
Xiuyun Guo
Monatshefte für Mathematik, 2011, 162 : 329 - 339

← 1 2 3 4 5 →