Geodesic
Subextensions for co-induced modules
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 554-560.

Voir la notice de l'article provenant de la source Math-Net.Ru

Using cohomological methods, we find a criterion for the embedding of a group extension with abelian kernel into the split extension of a co-induced module. This generalises some earlier similar results. We also prove an assertion about the conjugacy of complements in split extensions of co-induced modules. Both results follow from a relation between homomorphisms of certain cohomology groups.
Keywords: subextension, co-induced module, group cohomology. 
@article{SEMR_2018_15_a14,
     author = {Andrei V. Zavarnitsine},
     title = {Subextensions for co-induced modules},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {554--560},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a14/}
}
TY  - JOUR
AU  - Andrei V. Zavarnitsine
TI  - Subextensions for co-induced modules
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 554
EP  - 560
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a14/
LA  - en
ID  - SEMR_2018_15_a14
ER  - 
%0 Journal Article
%A Andrei V. Zavarnitsine
%T Subextensions for co-induced modules
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 554-560
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a14/
%G en
%F SEMR_2018_15_a14
Andrei V. Zavarnitsine. Subextensions for co-induced modules. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 554-560. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a14/

[1] D. J. Benson, Representations and cohomology. I: Basic representation theory of finite groups and associative algebras, Cambridge Studies in Advanced Mathematics, 30, Cambridge University Press, Cambridge, 1998 | MR | Zbl

[2] K. S. Brown, Cohomology of groups, Graduate Texts in Mathematics, 87, Springer-Verlag, New York, 1982 | DOI | MR | Zbl

[3] L. Kaloujnine, M. Krasner, “Le produit complet des groupes de permutations et le problème d'extension des groupes”, C. R. Acad. Sci. Paris, 227 (1948), 806–808 | MR | Zbl

[4] C. R. Leedham-Green, S. McKay, The structure of groups of prime power order, London Mathematical Society Monographs. New Series, 27, Oxford University Press, Oxford, 2002 | MR | Zbl

[5] D. J. S. Robinson, A course in the theory of groups, Graduate Texts in Mathematics, 80, 2nd ed., Springer-Verlag, New York, 1996 | DOI | MR

[6] M. Suzuki, Group theory I, Grundlehren der Mathematischen Wissenschaften, 247, Springer-Verlag, Berlin–Heidelberg–New York, 1982 | DOI | MR | Zbl

[7] C. A. Weibel, An introduction to homological algebra, Cambridge Studies in Advanced Mathematics, 38, Cambridge University Press, Cambridge, 1994 | MR | Zbl

[8] A. V. Zavarnitsine, “Subextensions for a permutation $PSL_2(q)$-module”, Sib. Elect. Math. Reports, 10 (2013), 551–557 | MR | Zbl

[9] A. V. Zavarnitsine, “Embedding central extensions of simple linear groups into wreath products”, Sib. Elect. Math. Reports, 13 (2016), 361–365 | MR | Zbl

[10] A. V. Zavarnitsine, “On the embedding of central extensions into wreath products”, Sib. Math. J., 58:5 (2017), 813–816 | DOI | Zbl