Geodesic
A Classification Of n -Abelian Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1238-1244

Voir la notice de l'article provenant de la source Cambridge University Press

The concept of an abelian group is central to group theory. For that reason many generalizations have been considered and exploited. One, in particular, is the idea of an n-abelian group (6). If n is an integer and n > 1, then a group G is n-abelian if, and only if,(xy)n = xnyn for all elements x and y of G. Thus, a group is 2-abelian if, and only if, it is abelian, while non-abelian n-abelian groups do exist for every n > 2.Many results pertaining to the way in which groups can be constructed from abelian groups can be generalized to theorems on n-abelian groups (1; 2). Moreover, the case of n = p, a prime, is useful in the study of finite p-groups (3; 4; 5). Moreover, a recent result of Weichsel (9) gives a description of all p-abelian finite p-groups. 
Alperin, J. L. A Classification Of n -Abelian Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 1238-1244. doi: 10.4153/CJM-1969-136-1
@article{10_4153_CJM_1969_136_1,
     author = {Alperin, J. L.},
     title = {A {Classification} {Of} n {-Abelian} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {1238--1244},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-136-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-136-1/}
}
TY  - JOUR
AU  - Alperin, J. L.
TI  - A Classification Of n -Abelian Groups
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 1238
EP  - 1244
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-136-1/
DO  - 10.4153/CJM-1969-136-1
ID  - 10_4153_CJM_1969_136_1
ER  - 
%0 Journal Article
%A Alperin, J. L.
%T A Classification Of n -Abelian Groups
%J Canadian journal of mathematics
%D 1969
%P 1238-1244
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-136-1/
%R 10.4153/CJM-1969-136-1
%F 10_4153_CJM_1969_136_1

[1] 1. Baer, Reinhold, Endlichkeitskriterien fur Kommutatorgruppen, Math. Ann. 124 (1952), 161–167. Google Scholar

[2] 2. Baer, Reinhold, Factorizations of n-soluble and n-nilpotent groups, Proc. Amer. Math. Soc. 4 (1953), 15–26. Google Scholar

[3] 3. Griïn, Otto, Beitrâge zur Gruppentheorie. IV. Uber eine Characterische Untergruppe, Math. Nach. 3 (1949), 77–94. Google Scholar

[4] 4. Griïn, Otto, Beitrâge zur Gruppentheorie. V, Osaka Math. J. 5 (1953), 117–146 Google Scholar

[5] 5. Hobby, C., A characteristic subgroup of a p-group, Pacific J. Math. 10 (1960), 853–858. Google Scholar

[6] 6. Levi, F., Notes on group theory. I, J. Indian Math. Soc. 8 (1944), 1–7 Google Scholar

[7] 7. Levi, F., Notes on group theory. VU, J. Indian Math. Soc. 9 (1945), 37–42 Google Scholar

[8] 8. Trotter, H. F., Groups in which raising to a power is an automorphism, Can. Math. Bull. 8 (1965), 825–827. Google Scholar

[9] 9. Weichsel, P. M., On p-abelian groups, Proc. Amer. Math. Soc. 18 (1967), 736–737. Google Scholar

Cité par Sources :