Some structural results on the non-abelian tensor square of groups

被引：37

作者：

Blyth, Russell D. ^{[1
]}

Fumagalli, Francesco ^{[2
]}

Morigi, Marta ^{[3
]}

机构：

[1] St Louis Univ, Dept Math & Comp Sci, St Louis, MO 63103 USA

[2] Univ Florence, Dipartimento Matemat Ulisse Dini, I-50134 Florence, Italy

[3] Univ Bologna, Dipartimento Matemat, I-40127 Bologna, Italy

来源：

JOURNAL OF GROUP THEORY | 2010年 / 13卷 / 01期

关键词：

PRODUCTS;

D O I：

10.1515/JGT.2009.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the non-abelian tensor square G circle times G for the class of groups G that are finitely generated modulo their derived subgroup. In particular, we find conditions on G/G' so that GnG is isomorphic to the direct product of del(G) and the non-abelian exterior square G Lambda G. For any group G, we characterize the non-abelian exterior square G Lambda G in terms of a presentation of G. Finally, we apply our results to some classes of groups, such as the classes of free solvable and free nilpotent groups of finite rank, and some classes of finite p-groups.

引用

页码：83 / 94

页数：12

共 50 条

[1] Cayley Graph for the Non-Abelian Tensor Square of Some Finite Groups
Zulkarnain, A.
Sarmin, N. H.
Hassim, H. I. Mat
Erfanian, A.
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2020, 44 (06) : 867 - 873
[2] On some series of a group related to the non-abelian tensor square of groups
Bastos, R.
de Oliveira, R.
Monetta, C.
Rocco, N. R.
JOURNAL OF ALGEBRA, 2022, 598 : 236 - 253
[3] THE NON-ABELIAN TENSOR SQUARE OF A FREE PRODUCT OF GROUPS
GILBERT, ND
ARCHIV DER MATHEMATIK, 1987, 48 (05) : 369 - 375
[4] The non-abelian tensor square of residually finite groups
Bastos, R.
Rocco, N. R.
MONATSHEFTE FUR MATHEMATIK, 2017, 183 (01): : 61 - 69
[5] The non-abelian tensor square of residually finite groups
R. Bastos
N. R. Rocco
Monatshefte für Mathematik, 2017, 183 : 61 - 69
[6] Non-abelian tensor square of finite-by-nilpotent groups
Raimundo Bastos
Noraí R. Rocco
Archiv der Mathematik, 2016, 107 : 127 - 133
[7] Non-abelian tensor square of finite-by-nilpotent groups
Bastos, Raimundo
Rocco, Norai R.
ARCHIV DER MATHEMATIK, 2016, 107 (02) : 127 - 133
[8] Non-Abelian tensor square and related constructions of p-groups
Bastos, R.
de Melo, E.
Goncalves, N.
Nunes, R.
ARCHIV DER MATHEMATIK, 2020, 114 (05) : 481 - 490
[9] Non-Abelian tensor square and related constructions of p-groups
R. Bastos
E. de Melo
N. Gonçalves
R. Nunes
Archiv der Mathematik, 2020, 114 : 481 - 490
[10] CHARACTERIZATION OF FINITE p-GROUPS BY THEIR NON-ABELIAN TENSOR SQUARE
Jafari, S. H.
Saeedi, F.
Khamseh, E.
COMMUNICATIONS IN ALGEBRA, 2013, 41 (05) : 1954 - 1963

← 1 2 3 4 5 →