Geodesic
Automorphisms of nonsplit coverings of $PSL_2(q)$ in odd characteristic dividing $q-1$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 285-291.

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We classify the nonsplit extensions of elementary abelian $p$-groups by $\operatorname{PSL}_2(q)$, with odd $p$ dividing $q-1$, for an irreducible induced action, calculate the relevant low-dimensional cohomology groups, and describe the automorphism groups of such extensions. 
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Andrei V. Zavarnitsine. Automorphisms of nonsplit coverings of $PSL_2(q)$ in odd characteristic dividing $q-1$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 285-291. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a11/

[1] V.P. Burichenko, “Extensions of abelian $2$-groups by $\operatorname{L}_2(q)$ with irreducible action”, Algebra Logic, 39:3 (2000), 160–183 | DOI | MR | Zbl

[2] V.P. Burichenko, “Nonsplit extensions of abelian $p$-groups by $L_2(p^n)$ and general theorems on extensions of finite groups”, Sib. Adv. Math., 25:2 (2015), 77–109 | DOI | MR | Zbl

[3] R. Burkhardt, “Die Zerlegungsmatrizen der Gruppen $PSL(2,p^f)$”, J. Algebra, 40:1 (1976), 75–96 | DOI | MR | Zbl

[4] J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of finite groups, Clarendon Press, Oxford, 1985 | MR | Zbl

[5] S. Deo, Algebraic topology. A primer, Texts and Readings in Mathematics, 27, Hindustan Book Agency, New Delhi; Springer, 2018 | DOI | MR | Zbl

[6] S.M. Gagola, “A splitting condition using block theory”, Mich. Math. J., 23:3 (1976), 203–206 | DOI | MR | Zbl

[7] K.W. Gruenberg, Cohomological topics in group theory, Lecture Notes in Mathematics, 143, Springer-Verlag, Berlin, etc., 1970 | DOI | MR | Zbl

[8] D.F. Holt, B. Eick, E.A. O'Brien, Handbook of computational group theory, Discrete Mathematics and its Applications, Chapman Hall/CRC Press, Boca Raton, 2005 | MR | Zbl

[9] B. Huppert, Finite groups. I, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, 134, Springer-Verlag, Berlin, etc., 1967 | DOI | Zbl

[10] B. Mortimer, “The modular permutation representations of the known doubly transitive groups”, Proc. Lond. Math. Soc., III. Ser., 41:1 (1980), 1–20 | DOI | MR | Zbl

[11] D.O. Revin, A.V. Zavarnitsine, “Automorphisms of nonsplit extensions of $2$-groups by $PSL_2(q)$”, J. Group Theory, 24:6 (2021), 1245–1261 | DOI | MR | Zbl

[12] D.J.S. Robinson, “Applications of cohomology to the theory of groups”, Groups. Conf. St. Andrews 1981, Lond. Math. Soc. Lect. Note Ser., 71, 1982, 46–80 | MR | Zbl

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