The Modular Group Algebra Problem for Small p-Groups Of Maximal Class
Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 1064-1078

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

We show that p-groups of maximal class and order p 5 are determined by their group algebras over the field of p elements. The most important information requisite for the proof is obtained from a detailed study of the unit group of a quotient algebra of the group algebra, larger than the small group algebra.
DOI : 10.4153/CJM-1996-055-x
Mots-clés : 20C05, 16S34, 16U60, 17B50, 20D15, 20F05, modular group algebra, p-group, isomorphism problem, maximal class
Salim, Mohamed A. M.; Sandling, Robert. The Modular Group Algebra Problem for Small p-Groups Of Maximal Class. Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 1064-1078. doi: 10.4153/CJM-1996-055-x
@article{10_4153_CJM_1996_055_x,
     author = {Salim, Mohamed A. M. and Sandling, Robert},
     title = {The {Modular} {Group} {Algebra} {Problem} for {Small} {p-Groups} {Of} {Maximal} {Class}},
     journal = {Canadian journal of mathematics},
     pages = {1064--1078},
     year = {1996},
     volume = {48},
     number = {5},
     doi = {10.4153/CJM-1996-055-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-055-x/}
}
TY  - JOUR
AU  - Salim, Mohamed A. M.
AU  - Sandling, Robert
TI  - The Modular Group Algebra Problem for Small p-Groups Of Maximal Class
JO  - Canadian journal of mathematics
PY  - 1996
SP  - 1064
EP  - 1078
VL  - 48
IS  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-055-x/
DO  - 10.4153/CJM-1996-055-x
ID  - 10_4153_CJM_1996_055_x
ER  - 
%0 Journal Article
%A Salim, Mohamed A. M.
%A Sandling, Robert
%T The Modular Group Algebra Problem for Small p-Groups Of Maximal Class
%J Canadian journal of mathematics
%D 1996
%P 1064-1078
%V 48
%N 5
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1996-055-x/
%R 10.4153/CJM-1996-055-x
%F 10_4153_CJM_1996_055_x

[1] 1. Bagiriski, C. and Caranti, A., The modular group algebras ofp-groups of maximal class, Canad. J., Math. 40(1988), 1422–1435. Google Scholar

[2] 2. Bagiriski, C., Modular group algebras of 2-groups of maximal class, Comm., Algebra 20(1992), 1229. 1241. Google Scholar

[3] 3. Blackburn, N., On a special class ofp-groups, Acta, Math. 100(1958), 45–92. Google Scholar

[4] 4. Cannon, J.J., An introduction to the group theory language, Cayley. In: Computational Group Theory, (ed. Atkinson, M.D.), Academic Press, London, 1984. 145–183. Google Scholar

[5] 5. Du, X., The centers of a radical ring, Canad. Math., Bull. 35(1992), 174–179. Google Scholar

[6] 6. Huppert, B., Endliche Gruppen I, Springer, Berlin, 1967. Google Scholar

[7] 7. Jacobson, N., Lie Algebras, Dover, New York, 1979. Google Scholar

[8] 8. James, R., The groups of order p6 (pan odd prime), Math., Comp. 34(1980), 613–637. Google Scholar

[9] 9. Michler, G.O., Newman, M.F. and O'Brien, E.A., Modular group algebras, unpublished report, Australian National Univ., Canberra, 1987. Google Scholar

[10] 10. Roggenkamp, K.W. and Scott, L.L., Automorphisms and nonabelian cohomology: an algorithm, Linear Algebra, Appl. 192(1993), 355–382. Google Scholar

[11] 11. Salim, M.A.M.and Sandling, R., The unit group of the modular small group algebra, Math. J. Okayama Univ., to appear. Google Scholar

[12] 12. Sandling, R., The isomorphism problem for group rings: a survey. In: Orders and Their Applications, Oberwolfach, 1984. (eds. Reiner, I. and Roggenkamp, K.W.), Lecture Notes in Math. 1142, Springer, Berlin, 1985. 256–288. Google Scholar

[13] 13. Sandling, R., The modular group algebra of a central-elementary-by-abelian p-group, Arch. Math., (Basel) 52(1989), 22–27. Google Scholar

[14] 14. Sandling, R., The modular group algebra problem for metacy die p-groups, Proc. Amer. Math., Soc. 124(1996), 1347–1350. Google Scholar

[15] 15. Wursthorn, M., Die modularen Gruppenringe der Gruppen der Ordnung 26, Diplomarbeit, Universitat Stuttgart, 1990. Google Scholar

[16] 16. Wursthorn, M., Isomorphisms of modular group algebras: An algorithm and its application to groups of order 26, J. Symb., Comput. 15(1994), 211–227. Google Scholar

Cité par Sources :