Shunkov groups saturated with general linear groups. (English. Russian original) Zbl 1347.20038

Sib. Math. J. 57, No. 1, 174-184 (2016); translation from Sib. Mat. Zh. 57, No. 1, 222-235 (2016).
Summary: We prove that if a periodic Shunkov group is saturated with degree 2 general linear groups over finite fields then it is isomorphic to the degree 2 general linear group over a suitable locally finite field.


20F50 Periodic groups; locally finite groups
20G15 Linear algebraic groups over arbitrary fields
20E25 Local properties of groups
20E07 Subgroup theorems; subgroup growth
20G40 Linear algebraic groups over finite fields
Full Text: DOI


[1] Shlepkin, A. K., Conjugately biprimitive finite groups containing finite unsolvable subgroups, 363, (1993)
[2] Rubashkin, A. G.; Filippov, K. A., Periodic groups saturated with the groups \(L\)_{2}(\(p\)\^{}{n}), Sib. Math. J., 46, 1119-1122, (2005) · Zbl 1118.20039
[3] Shlepkin, A. A.; Sabodakh, I. V., On shunkov groups saturated with GL2(pn), Sib. Elektron. Mat. Izv., 11, 734-744, (2014) · Zbl 1330.20059
[4] Shlepkin, A. A., The groups saturated by GL_{2}(\(p\)\^{}{n}), Vestnik SibGAU, 1, 100-108, (2013)
[5] Shunkov, V. P., On a class of \(p\)-groups, Algebra and Logic, 9, 291-297, (1970) · Zbl 0237.20032
[6] Kuznetsov, A. A.; Filippov, K. A., Groups saturated by a given set of groups, Sib. Elektron. Mat. Izv., 8, 230-246, (2011) · Zbl 1329.20048
[7] Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York; Heidelberg; Berlin (1977). · Zbl 0499.20001
[8] Kuznetsov A. A., Lytkina D. V., Tukhvatullina L. R., and Filippov K. A., Groups with Saturation Condition [in Russian], KrasGAU, Krasnoyarsk (2010). · Zbl 1154.20037
[9] Shunkov, V. P., On periodic groups with an almost regular involution, Algebra and Logic, 11, 260-272, (1972) · Zbl 0275.20074
[10] Shlepkin, A. A., Periodic groups saturated by wreathed groups, Sib. Elektron. Mat. Izv., 10, 56-64, (2013) · Zbl 1330.20058
[11] Shlepkin, A. A., On the periodic groups saturated with projective linear groups PGL_{2}(\(p\)\^{}{n}), Sib. Math. J., 55, 761-764, (2015) · Zbl 1328.20059
[12] Dickson L., Linear Groups, B. G. Teubner, Leipzig (1901). · JFM 32.0134.03
[13] Carter R. W., Simple Groups of Lie Type, John Wiley and Sons, London (1972). · Zbl 0248.20015
[14] Harada, K.; Mong, L. L., Indecomposable Sylow 2-subgroups of simple groups, Acta Appl. Math., 85, 161-194, (2005) · Zbl 1086.20009
[15] Duzh, A. A.; Shlepkin, A. A., Shunkov’s groups saturated by direct products of groups, Vladikavkaz. Mat. Zh., 12, 123-126, (2012) · Zbl 1326.20041
[16] Lytkina, D. V., On the periodic groups saturated by direct products of finite simple groups. II, Sib. Math. J., 52, 871-883, (2011) · Zbl 1247.20047
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.