Page 299 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
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GRAPHS AND GROUPS, GEOMETRIES AND GAP - G2G2 (MS-7)
a subgroup of a group t Zi Symni, where Zi ∈ {1, C3} for each i, such that H projects
i=1
t
onto i=1 S ymni , and we have obtained a criterium of pronormality of such a subgroup in
such a group [10]. All these works were supported by the Russian Science Foundation (project
19-71-10067). These investigations give a rise to researches on effective algorithms (to be
implemented in GAP) for deciding the pronormality of a subgroup of odd index in a finite
simple group. This is a joint project with Stephen Glasby and Cheryl E. Praeger.
References
[1] L. Babai, Isomorphism problem for a class of point-symmetric structures, Acta Math.
Acad. Sci. Hungar. 29 (1977) 329–336.
[2] W. Guo, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd index in
some extensions of finite groups, Siberian Math. J. 59:4 (2018) 610–622.
[3] W. Guo, D. O. Revin, Pronormality and submaximal X-subgroups in finite groups, Com-
munications in Mathematics and Statistics. 6:3 (2018) 289–317.
[4] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple groups, Siberian Math. J. 56:6 (2015) 1101–1107.
[5] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, A pronormality criterion for supplements
to abelian normal subgroups, Proc. Steklov Inst. Math. Suppl. 296:1 (2017) S145–S150.
[6] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple symplectic groups, Siberian Math. J. 58:3 (2017) 467–475.
[7] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On pronormal subgroups in finite simple
groups, Doklady Mathematics. 98:2 (2018) 405–408.
[8] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple groups, Groups St Andrews 2017 in Birmingham (Birmingham, 5th-
13th August 2017), London Mathematical Society Lecture Note Series, 455, eds. C. M.
Campbell, M. R. Quick, C. W. Parker, E. F. Robertson, C. M. Roney-Dougal, Cambridge
University Press, Cambridge, 2019, P. 406–418.
[9] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, Finite simple exceptional groups of Lie type
in which all the subgroups of odd index are pronormal, arXiv:1910.02524v2 [math.GR].
[10] N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd index in some direct
products of finite groups, in preparation.
[11] P. P. Palfy, isomorphism problem for relational structures with a cyclic automorphism,
Europ. J. Combinatorics. 8 (1987) 35–43.
[12] Ch. E. Praeger, On transitive permutation groups with a subgroup satisfying a certain
conjugacy condition, J. Austral. Math. Soc. 36:1 (1984) 69–86.
[13] E. P. Vdovin, D. O. Revin, Pronormality of Hall subgroups in finite simple groups,
Siberian Math. J. 53:3 (2012) 419–430.
297
a subgroup of a group t Zi Symni, where Zi ∈ {1, C3} for each i, such that H projects
i=1
t
onto i=1 S ymni , and we have obtained a criterium of pronormality of such a subgroup in
such a group [10]. All these works were supported by the Russian Science Foundation (project
19-71-10067). These investigations give a rise to researches on effective algorithms (to be
implemented in GAP) for deciding the pronormality of a subgroup of odd index in a finite
simple group. This is a joint project with Stephen Glasby and Cheryl E. Praeger.
References
[1] L. Babai, Isomorphism problem for a class of point-symmetric structures, Acta Math.
Acad. Sci. Hungar. 29 (1977) 329–336.
[2] W. Guo, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd index in
some extensions of finite groups, Siberian Math. J. 59:4 (2018) 610–622.
[3] W. Guo, D. O. Revin, Pronormality and submaximal X-subgroups in finite groups, Com-
munications in Mathematics and Statistics. 6:3 (2018) 289–317.
[4] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple groups, Siberian Math. J. 56:6 (2015) 1101–1107.
[5] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, A pronormality criterion for supplements
to abelian normal subgroups, Proc. Steklov Inst. Math. Suppl. 296:1 (2017) S145–S150.
[6] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple symplectic groups, Siberian Math. J. 58:3 (2017) 467–475.
[7] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On pronormal subgroups in finite simple
groups, Doklady Mathematics. 98:2 (2018) 405–408.
[8] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd
index in finite simple groups, Groups St Andrews 2017 in Birmingham (Birmingham, 5th-
13th August 2017), London Mathematical Society Lecture Note Series, 455, eds. C. M.
Campbell, M. R. Quick, C. W. Parker, E. F. Robertson, C. M. Roney-Dougal, Cambridge
University Press, Cambridge, 2019, P. 406–418.
[9] A. S. Kondrat’ev, N. V. Maslova, D. O. Revin, Finite simple exceptional groups of Lie type
in which all the subgroups of odd index are pronormal, arXiv:1910.02524v2 [math.GR].
[10] N. V. Maslova, D. O. Revin, On the pronormality of subgroups of odd index in some direct
products of finite groups, in preparation.
[11] P. P. Palfy, isomorphism problem for relational structures with a cyclic automorphism,
Europ. J. Combinatorics. 8 (1987) 35–43.
[12] Ch. E. Praeger, On transitive permutation groups with a subgroup satisfying a certain
conjugacy condition, J. Austral. Math. Soc. 36:1 (1984) 69–86.
[13] E. P. Vdovin, D. O. Revin, Pronormality of Hall subgroups in finite simple groups,
Siberian Math. J. 53:3 (2012) 419–430.
297
