Realization of even permutations of even degree by products of four involutions without fixed points

References

[1] Bourbaki N., Groupes et Algèbres de Lie. Chapitres 4, 5 et 6, Hermann, Paris, 1968, 282 pp.Search in Google Scholar

[2] Artin E., Geometric algebra, M.: Nauka, 1969 (in Russian), 288 pp.Search in Google Scholar

[3] Halmos P. R., Kakutani S., “Products of symmetries”, Bull. Amer. Math. Soc., 64 (1958), 77–78.10.1090/S0002-9904-1958-10156-1Search in Google Scholar

[4] Radjavi H., “Products of Hermitian matrices and symmetries”, Proc. Amer. Math. Soc., 21 (1969), 369–372.10.1090/S0002-9939-1969-0240116-9Search in Google Scholar

[5] Sampson A. R., “A note on a new matrix decomposition”, Linear Algebra Appl., 8 (1974), 459–463.10.1016/0024-3795(74)90079-2Search in Google Scholar

[6] Waterhouse W. C., “Factoring unimodular matrices”, Advanced Problem 5876, Solution, Am. Math. Mon., 81 (1974), 1035.10.2307/2319325Search in Google Scholar

[7] Gustafson W. H., Halmos P. R., “Products of involutions”, Linear Algebra Appl., 13:1–2 (1976), 157–162.10.1016/0024-3795(76)90054-9Search in Google Scholar

[8] Moran G., “Permutations as products of k conjugate involutions”, J. Comb. Theory Ser. A., 19:2 (1975), 240–242.10.1016/S0097-3165(75)80015-XSearch in Google Scholar

[9] Borel A., Carter R., Curtis C. W., Iwahori N., Springer T. A., Steinberg R., Seminar on Algebraic Groups and Related Finite Groups, Lect. Notes Math., 131, Springer, 1970, 326 pp.10.1007/BFb0081541Search in Google Scholar

[10] Petrov N. T., “On the length of simple groups”, Sov. Math. Dokl., 14 (1973), 127–131.Search in Google Scholar

[11] Dénes J., “The representation of a permutation as the product of a minimal number of transpositions, and its connection with the theory of graphs”, Publ. Math. Inst. Hungar. Acad. Sci., 4 (1959), 63–70.Search in Google Scholar

[12] Pikar S., “On bases of the symmetric group”, Kiberneticheskiy sb. Novaya seriya, 1, M.: Mir, 1965, 7–34 (in Russian).Search in Google Scholar

[13] Kapelmakher V. L., Lisovets V. A., “Sequential generation of substitutions by means of transposition basis”, Kibernetika, 3 (1975), 17–21 (in Russian).Search in Google Scholar

[14] Sushchanskiy V. I., Voskanyan R. A., “On systems of generating symmetric and alternating groups consisting of cycles of the same length”, Questions of group theory and homological algebra, Yaroslavl, 1985, 43–49 (in Russian).Search in Google Scholar

[15] Zubov A. Yu., “On the representation of substitutions as products ofa transposition and a full cycle”, J. Math. Sci., 166:6 (2010), 710–724.10.1007/s10958-010-9887-zSearch in Google Scholar

[16] Lugo M., Profiles of large combinatorial structures, PhD Thesis, Univ. Pensylvania, 2010.Search in Google Scholar

[17] Zubov A. Yu., “Circular inversions of permutations and their use in sorting problems”, Prikladnaya diskret. matem., 31:1 (2016), 13–30 (in Russian).10.17223/20710410/31/2Search in Google Scholar

[18] Mikhailov V. G., “The number of decomposition of random permutation into the product of two involutions with given cycle in one of multipliers”, Matematicheskie Voprosy Kriptografii, 8:1 (2017), 81–94.10.4213/mvk216Search in Google Scholar

[19] Bugay L., “Some involutions which generate the finite symmetric group”, Math. Sci. Appl. E-Notes, 8:1 (2020), 25–28.10.36753/mathenot.608443Search in Google Scholar