Current Research Interest – Algebra,
Infinite group theory:
Formation theory and Fitting classes
Wreath products
Burnside problems
Automorphism groups
Wielandt subgroup of a group
Groups with rank restrictions on subgroups
Groups with various minimal or maximal conditions
Products of groups
Groups with subgroups satisfying certain properties
Linear groups satisfying certain finiteness conditions
Main publications:
1. (with M. J. Evans and L. A. Kurdachenko) Linear groups with the minimal condition on subgroups of infinite central dimension, J. Algebra 277(2004), 172-186.
2. (with M. J. Evans and H. Smith) A finiteness condition on subgroups of large derived length, J. Algebra, 280 (2004), 762-771.
3. (with M. J. Evans and H. Smith) Embedding groups in locally (soluble-by-finite) simple groups, J. Group Theory, to appear.
4. (with M. J. Evans and H. Smith) Groups with all proper subgroups soluble-by-finite rank, J. Algebra, 289, (2005), 135-147.
5. (with M. J. Evans and H. Smith) Locally (soluble-by-finite) groups with various restrictions on subgroups of infinite rank, Glasgow Math. J. 47 (2005), 319-326.
M. R. Dixon, L. A. Kurdachenko, N. N. Semko, I. Ya. Subbotin, “On some topics in the theory of infinite dimensional linear groups”, Algebra Discrete Math., 29:1 (2020), 1–32
2017
2.
O. D. Artemovych, A. Ballester-Bolinches, M. R. Dixon, F. de Giovanni, R. I. Grigorchuk, V. V. Kirichenko, L. A. Kurdachenko, V. S. Monakhov, J. Otal, M. O. Perestyuk, A. P. Petravchuk, M. V. Pratsiovytyi, A. M. Samoilenko, A. N. Skiba, I. Ya. Subbotin, E. I. Zelmanov, A. V. Zhuchok, Yu. V. Zhuchok, “Nicolai N. Semko (dedicated to 60-th Birthday)”, Algebra Discrete Math., 24:1 (2017), C–F
2016
3.
Martyn R. Dixon, Leonid A. Kurdachenko, Aleksandr A. Pypka, Igor Ya. Subbotin, “Groups satisfying certain rank conditions”, Algebra Discrete Math., 22:2 (2016), 184–200
M. R. Dixon, V. V. Kirichenko, L. A. Kurdachenko, J. Otal, N. N. Semko, L. A. Shemetkov, I. Ya. Subbotin, “S. N. Chernikov and the development of infinite group theory”, Algebra Discrete Math., 13:2 (2012), 169–208
2010
5.
Martyn R. Dixon, Leonid A. Kurdachenko, Javier Otal, “On the existence of complements in a group to some abelian normal subgroups”, Algebra Discrete Math., 10:1 (2010), 18–41
2009
6.
Martyn R. Dixon, Igor Ya. Subbotin, “Groups with finiteness conditions on some subgroup systems: a contemporary stage”, Algebra Discrete Math., 2009, no. 4, 29–54
O. D. Artemovich, A. Ballester-Bolinches, V. A. Bovdi, M. R. Dixon, F. de Giovanni, R. I. Grigorchuk, L. A. Kurdachenko, F. N. Liman, P. Longobardi, M. Maj, V. S. Monakhov, J. Otal, A. P. Petravchuk, A. A. Pypka, A. Russo, N. N. Semko, A. N. Skiba, G. Vincenzi, E. I. Zel'manov, A. V. Zhuchok, Yu. V. Zhuchok, “Igor Ya. Subbotin (dedicated to 70th Birthday)”, Algebra Discrete Math., 29:2 (2020), C–F
9.
O. D. Artemovych, A. Ballester-Bolinches, V. A. Bovdi, M. R. Dixon, F. de Giovanni, R. I. Grigorchuk, W. Holubowski, F. M. Lyman, P. Longobardi, M. Maj, V. S. Monakhov, A. S. Oliynyk, B. V. Oliynyk, J. Otal, M. A. Perestyuk, A. P. Petravchuk, M. V. Pratsiovytyi, A. A. Pypka, A. Russo, A. M. Samoilenko, N. N. Semko, A. N. Skiba, I. Ya. Subbotin, G. Vincenzi, R. A. Zatorskii, E. I. Zel'manov, A. V. Zhuchok, Yu. V. Zhuchok, “Leonid A. Kurdachenko (dedicated to 70th Birthday)”, Algebra Discrete Math., 29:1 (2020), C–H
2010
10.
A. Ballester-Bolinches, N. N. Bilotskii, M. R. Dixon, R. I. Grigorchuk, V. V. Kirichenko, L. A. Kurdachenko, N. F. Kuzennyj, J. Otal, N. N. Semko, P. Shumyatsky, V. I. Sushchansky, E. I. Zel'manov, “Igor Ya. Subbotin: to the 60th birthday”, Algebra Discrete Math., 9:1 (2010), E–H
2009
11.
A. Ballester-Bolinches, R. I. Grigorchuk, M. R. Dixon, Yu. A. Drozd, V. V. Kirichenko, J. Otal, M. A. Perestyuk, A. P. Petravchuk, N. V. Polyakov, A. M. Samoilenko, N. N. Semko, V. V. Sharko, L. A. Shemetkov, A. N. Skiba, I. Ya. Subbotin, V. I. Sushchansky, E. I. Zel'manov, “Leonid A. Kurdachenko: to the 60th birthday”, Algebra Discrete Math., 2009, no. 4, E–H
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