On products of cyclic and abelian finite p-groups (p odd)

被引：1

作者：

McCann, Brendan ^{[1
]}

机构：

[1] Waterford Inst Technol, Dept Comp & Math, Cork Rd, Waterford, Ireland

来源：

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES | 2018年 / 94卷 / 08期

关键词：

Products of groups; factorised groups; finite p-groups;

D O I：

10.3792/pjaa.94.77

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an odd prime p, it is shown that if G = AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p(k), then Omega(k)(A)B (sic) G, where Omega(k)(A) = < g is an element of A vertical bar g(pk) = 1 >.

引用

页码：77 / 80

页数：4

共 50 条

[1] On Products of Cyclic and Non-Abelian Finite p-Groups
McCann, Brendan
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2020, 9 : 5 - 37
[2] On products of cyclic and elementary abelian p-groups
Mccann, Brendan
PUBLICATIONES MATHEMATICAE-DEBRECEN, 2017, 91 (1-2): : 185 - 216
[3] PROJECTIVITIES IN FINITE ABELIAN P-GROUPS
WEHRHAHN, KH
MATHEMATISCHE ZEITSCHRIFT, 1971, 123 (03) : 231 - &
[4] TORSION PRODUCTS OF ABELIAN P-GROUPS
CUTLER, D
JOURNAL OF ALGEBRA, 1982, 77 (01) : 158 - 161
[5] ABELIAN SUBGROUPS OF FINITE P-GROUPS
DANCS, SC
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 169 (NJUL) : 489 - &
[6] On automorphisms of finite abelian p-groups
Golasinski, Marek
Goncalves, Daciberg Lima
MATHEMATICA SLOVACA, 2008, 58 (04) : 405 - 412
[7] FINITE p-GROUPS AND CENTRALIZERS OF NON-CYCLIC ABELIAN SUBGROUPS
Wang, J.
Guo, X.
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2017, 43 (01): : 171 - 192
[8] p-groups of automorphisms of Abelian p-groups
Khukhro E.I.
Algebra and Logic, 2000, 39 (3) : 207 - 214
[9] Automorphism Groups of Finite Abelian p-groups and Transvections
Han, Gang
Zhou, Qipeng
COMMUNICATIONS IN ALGEBRA, 2016, 44 (04) : 1411 - 1419
[10] Large Abelian subgroups of finite p-groups
Glauberman, G
JOURNAL OF ALGEBRA, 1997, 196 (01) : 301 - 338

← 1 2 3 4 5 →