Polregularni elementi v 2-zaprtjih rešljivih grup / Semiregular elements in 2-closures of solvable groups

(SI) Pri obravnavi problemov iz algebraične teorije grafov, predvsem tistih o tranzitivnih grupnih delovanjih, najtežji del običajno predstavljajo nerešljive grupe, saj je v primeru rešljivih grup mogoče podati vsaj delne rezultate. Pri problemu polregularnosti je slika obrnjena. Tu glavno oviro za popolno rešitev problema predstavlja razred rešljivih grup. Cilj predlaganega projekta je podati nove usmeritve, ki bi trasirale pot do popolne rešitve problema polregularnosti, pri čemer bomo posebej natančno obravnavali tranzitivne rešljive grupe. Ta problem je poznan kot problem simultanega konjugiranja. Eden izmed ciljev predlaganega projekta je razviti učinkovite algoritme za reševanje problema simultanega konjugiranja v simetričnih grupah in najti netrivialne spodnje meje za ta problem. Smiselnost obravnave tega problema v okviru predlaganega projekta, leži v dejstvu, da znani Sridharjev algoritem ne deluje, če so vse permutacije v danih nizih polregularne.
(EN) With the semiregularity problem, however, the situation is completely reversed. It is the class of solvable groups that presents the main obstacle to obtaining a complete solution. The proposed project aims to make further steps towards complete solution of the semiregularity problem with special emphasis given to transitive solvable groups.The problem is known as the simultaneous conjugacy problem. One of the goals of the proposed project is to develop efficient algorithms for solving the simultaneous conjugacy problem in the symmetric group, and to find non-trivial lower bounds for this problem. It is natural to consider this problem in the framework of the proposed project as the Sridhar’s algorithm for solving the simultaneous conjugacy problem does not work in the case when every permutation in each of the arrays is semiregular.