Geodesic
Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups
Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 19-69.

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Let a group $\widetilde G$ be a nonsplit extension of an elementary Abelian $p$-group $V$ by the group $G=L_2(p^n)$ such that the action of $G$ on $V$ is irreducible. In the present article, we classify (up to isomorphism) such groups $\widetilde G$ with $p^n\ne3^4$. The main part of the article consists of proofs of numerous general assertions on representations, cohomologies, and extensions of finite groups. Further, we use these results in our study of extensions by $L_2(q)$. 
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     author = {V. P. Burichenko},
     title = {Nonsplit extensions of {Abelian} $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups},
     journal = {Matemati\v{c}eskie trudy},
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     year = {2014},
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     url = {http://geodesic.mathdoc.fr/item/MT_2014_17_1_a1/}
}
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V. P. Burichenko. Nonsplit extensions of Abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups. Matematičeskie trudy, Tome 17 (2014) no. 1, pp. 19-69. http://geodesic.mathdoc.fr/item/MT_2014_17_1_a1/

[1] Bakhturin Yu. A., Osnovnye struktury sovremennoi algebry, Nauka, M., 1990 | MR | Zbl

[2] Braun K. S., Kogomologii grupp, Nauka, M., 1987 | MR

[3] Burbaki N., Teoriya mnozhestv, Mir, M., 1965

[4] Burichenko V. P., “Rasshireniya abelevoi 2-gruppy s pomoschyu $L_2(q)$ s neprivodimym deistviem”, Algebra i logika, 39:3 (2000), 280–319 | MR | Zbl

[5] Burichenko V. P., “O prostranstvakh $\mathrm{Ext}$ dlya gruppy $\mathrm{SL}(2,q)$”, Matem. tr., 16:1 (2013), 28–55 | MR

[6] Godeman R., Algebraicheskaya topologiya i teoriya puchkov, Izd-vo inostr. lit., M., 1961 | MR

[7] Dëdonne Zh., Geometriya klassicheskikh grupp, Mir, M., 1974 | MR

[8] Kartan A., Eilenberg S., Gomologicheskaya algebra, Izd-vo inostr. lit., M., 1960 | MR

[9] V. D. Mazurov (red.), Kourovskaya tetrad, Nereshennye voprosy teorii grupp, 12-e izd., Institut matematiki SO RAN, Novosibirsk, 1992 | MR | Zbl

[10] Kuzmin Yu. V., Gomologicheskaya teoriya grupp, Faktorial press, M., 2006

[11] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[12] Leng S., Algebra, Mir, M., 1968

[13] Maklein S., Gomologiya, Mir, M., 1966

[14] Steinberg R., Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR | Zbl

[15] Feit U., Teoriya predstavlenii konechnykh grupp, Nauka, M., 1990 | MR | Zbl

[16] Brauer R., Nesbitt C., “On the modular characters of groups”, Ann. of Math. (2), 42 (1941), 556–590 | DOI | MR | Zbl

[17] Carlson J. F., “The cohomology of irreducible modules over $\mathrm{SL}(2,p^n)$”, Proc. London Math. Soc. (3), 47:3 (1983), 480–492 | DOI | MR | Zbl

[18] Curtis C. W., Reiner I., Methods of Representation Theory, John Wiley Sons, Inc., New York, 1990 | MR | Zbl

[19] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin–New York, 1992 | MR