The classification of Abelian and nilpotent subgroups of all finite simple groups, except sporadic, is completed. We found orders, structure, and classes of Abelian and nilpotent subgroups of maximal orders. The classification of Abelian subgroups of maximal order in unipoted subgroups of groups of Lie type, started by Barry and Wong, is completed. We found orders, structure, and classes. We also gave clear uniform way of finding abelian unipotent subgroups of maximal order in all groups of Lie type. Togeather with D. O. Revin the classification of finite $E_\pi$ and $D_\pi$ groups is completed. Togeather with M. C. Tamburini significant progress in solving problem on conjugacy of Carter subgroups in finite groups is obtained.
Main publications:
W. Guo, E. P. Vdovin, “Carter subgroups and Fitting heights of finite groups”, Archiv der Mathematik, 110:5 (2018), 427–432
W. Guo, E. P. Vdovin, “Number of Sylow subgroups in finite groups”, Journal of Group Theory, 21:4 (2018), 695–712
W. Guo, D. O. Revin, E. P. Vdovin, “Confirmation for Wielandts conjecture”, Journal of Algebra, 434 (2015), 193–206
E. P. Vdovin, “The structure of groups possessing Carter subgroups of odd order”, Algebra and Logic, 54:2 (2015), 105–107
E. P. Vdovin, “Groups of induced automorphisms and their application to studying the existence problem for Hall subgroups”, Algebra and Logic, 53:5 (2014), 418–421
D. O. Revin, E. P. Vdovin, “Frattini argument for Hall subgroups”, Journal of Algebra, 414:1 (2014), 95–104
I. P. Ivanov, E. P. Vdovin, “Classification of finite reparametrization symmetry groups in the three-Higgs-doublet model”, The European Phisical Journal C, 73 (2013), 2309 , 25 pp.
E. P. Vdovin, “On intersection of solvable Hall subgroups in finite simple exceptional groups of Lie type”, Proc. Steklov Inst. Math. (Suppl.), 285, suppl. 1 (2014), S183–S190
E. P. Vdovin, “On the base size of a transitive group with solvable point stabilizer”, Journal of Algebra and its Application, 11:1 (2012), 1250015 , 14 pp.
I. P. Ivanov, V. Keus, E. P. Vdovin, “Abelian symmetries in multi-Higgs-doublet models”, J. Phys. A: Math. Theor., 45:12 (2012), 2152001 , 29 pp.
A. V. Vasil'ev, E. P. Vdovin, “Cocliques of maximal size in the prime graph of a finite simple group”, Algebra and Logic, 50:4 (2011), 291–322
E. P. Vdovin, D. O. Revin, “Theorems of Sylow type”, Russian Math. Surveys, 66:5 (2011), 829–870
D. O. Revin, E. P. Vdovin, “An existence criterion for Hall subgroups of finite groups”, Journal of Group Theore, 14:1 (2011), 93–101
E. P. Vdovin, D. O. Revin, “A conjugacy criterion for Hall subgroups in finite groups”, Siberian Math. J., 51:3 (2010), 402–409
D. O. Revin, E. P. Vdovin, “On the number of classes of conjugate Hall subgroups in finite simple groups”, Journal of algebra, 324:12 (2010), 3614–3652
E. P. Vdovin, V. I. Zenkov, “On the intersections of solvable Hall subgroups in finite groups”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S234–S243
E. P. Vdovin, A. A. Gal't, “Normalizers of subsystem subgroups in finite groups of Lie type”, Algebra and Logic, 47:1 (2008), 1–17
E. P. Vdovin, “Carter subgroups of finite groups”, Siberian Adv. Math., 19:1 (2009), 24–74
E. P. Vdovin, “Carter subgroups of finite almost simple groups”, Algebra and Logic, 46:2 (2007), 90–119
E. P. Vdovin, “On the existence of Carter subgroups”, Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S195–S203
E. P. Vdovin, “O probleme sopryazhennosti dlya karterovykh podgrupp”, Sib. matem. zhurn., 47:4 (2006), 725–730
A. V. Vasil'ev, E. P. Vdovin, “An Adjacency Criterion for the Prime Graph of a Finite Simple Group”, Algebra and Logic, 44:6 (2005), 381–406
A. Previtali, M. C. Tamburini, E. P. Vdovin, “The Carter subgroups of some classical groups”, Bulletin of London Mathematical Society, 36:2 (2004), 145–155
E. P. Vdovin, “The number of subgroups with trivial unipotent radicals in finite groups of Lie type”, Journal of Group Theory, 7:1 (2004), 99–112
E. P. Vdovin, D. O. Revin, “Hall subgroups of odd order in finite groups”, Algebra and Logic, 41:1 (2002), 8–29
M. C. Tamburini, E. P. Vdovin, “Carter subgroups in finite groups”, Journal of algebra, 255:1 (2002), 148–163 (to appear)
E. P. Vdovin, “Large Abelian Unipotent Subgroups of Finite Chevalley Groups”, Algebra and Logic, 40:5 (2001), 292–305
E. P. Vdovin, “Maximal Orders of Abelian Subgroups in Finite Chevalley Groups”, Math. Notes, 69:4 (2001), 475–498
E. P. Vdovin, “Large nilpotent subgroups of finite simple groups”, Algebra and Logic, 39:5 (2000), 301–312
E. P. Vdovin, “Maximal orders of abelian subgroups in finite simple groups”, Algebra and logic, 2:2 (1999), 67–83
