Uniform cyclic group factorizations of finite groups

References

• Bohli, J. M., Steinwandt, R., González Vasco, M. I., Martínez, C. Weak keys in MST1. Des. Codes Cryptogr 37(3): 509–524. DOI: 10.1007/s10623-004-4040-y.
   Web of Science ®Google Scholar
• Burness, T. C., Li, C. H. (2021). On solvable factors of almost simple groups. Adv. Math. 377:Paper No. 107499, 36 pp. DOI: 10.1016/j.aim.2020.107499.
   Web of Science ®Google Scholar
• Conway, J. H., Curtis, R. T., Norton, S. P., Parker, R. A., Wilson, R. A. (1985). An ATLAS of Finite Groups. Oxford: Oxford University Press.
   Google Scholar
• Dixon, J. D. (2008). Generating random elements in finite groups. Electron. J. Comb. 15:R94–R94.
   Web of Science ®Google Scholar
• Dixon, J. D., Mortimer, B. (1996). Permutation Groups. Graduate Texts in Mathematics, 163. New York: Springer-Verlag, xii + 346 pp.
   Google Scholar
• Gentchev, Ts. R. (1986). Factorizations of the sporadic simple groups. Arch. Math. (Basel) 47:97–102. DOI: 10.1007/BF01193676.
   Web of Science ®Google Scholar
• Gentchev, Ts. R. (1986). Factorizations of the groups of Lie type of Lie rank 1 or 2. Arch. Math. (Basel) 47:439–499. DOI: 10.1007/BF01189858.
   Web of Science ®Google Scholar
• Giudici, M. (2006). Factorisations of sporadic simple groups. J. Algebra 304:311–323. DOI: 10.1016/j.jalgebra.2006.04.019.
   Web of Science ®Google Scholar
• González Vasco, M. I., Rötteler, M., Steinwandt, R. (2003). On minimal length factorizations of finite groups. Exp. Math. 12(1):1–12. DOI: 10.1080/10586458.2003.10504708.
   Web of Science ®Google Scholar
• González Vasco, M. I., Steinwandt, R. (2002). Obstacles in two public-key cryptosystems based on group factorizations. Tatra Mt. Math. Publ. 25:23–37.
   Google Scholar
• Gorenstein, D. (2007). Finite Groups, 301. Providence, RI: American Mathematical Society.
   Google Scholar
• Hering, C., Liebeck, M. W., Saxl, J. (1987). The factorizations of the finite exceptional groups of Lie type. J. Algebra 106(2):517–527. DOI: 10.1016/0021-8693(87)90013-5.
   Web of Science ®Google Scholar
• Holmes, P. E. (2003). On minimal factorisations of sporadic groups. Exp. Math. 13(4):435–440. DOI: 10.1080/10586458.2004.10504552.
   Web of Science ®Google Scholar
• Holt, D., Rowley, P. (1993). On products of Sylow subgroups in finite groups. Arch. Math. (Basel) 60(2):105–107. DOI: 10.1007/BF01199094.
   Web of Science ®Google Scholar
• Itô, N. (1953). On the factorizations of the linear fractional group LF(2,pn). Acta Sci. Math. (Szeged) 15:79–84.
   Google Scholar
• Lempken, W., van Trung, T. (2005). On minimal logarithmic signatures of finite groups. Exp. Math. 14(3):257–269. DOI: 10.1080/10586458.2005.10128924.
   Web of Science ®Google Scholar
• Lempken, W., van Trung, T., Magliveras, S. S., Wandi, W. (2009). A public key cryptosystem based on non-abelian finite groups. J. Cryptology 22(1):62–74. DOI: 10.1007/s00145-008-9033-y.
   Web of Science ®Google Scholar
• Li, C. H., Xia, B. (2019). Factorizations of almost simple groups with a factor having many non-solvable composition factors. J. Algebra 528:439–473. DOI: 10.1016/j.jalgebra.2019.03.012.
   Web of Science ®Google Scholar
• Li, C. H., Xia, B. (2022). Factorizations of almost simple groups with a solvable factor, and Cayley graphs of solvable groups. Mem. Amer. Math. Soc. 279(432):iv + 99 pp.
   Google Scholar
• Liebeck, M. W., Praeger, C. E., Saxl, J. (1990). The maximal factorizations of the finite simple groups and their automorphism groups. Mem. Amer. Math. Soc. 86(432):iv + 151 pp. DOI: 10.1090/memo/0432.
   Web of Science ®Google Scholar
• Magliveras, S. S. (1986). A cryptosystem from logarithmic signatures of finite groups. In: Proceedings of the 29th Midwest Symposium on Circuits and Systems, pp. 972–975.
   Google Scholar
• Magliveras, S. S. (2002). Secret and public-key cryptosystems from group factorizations. Tatra Mt. Math. Publ. 25:1–12.
   Google Scholar
• Magliveras, S. S., Stinson, D. R., van Trung, T. (2002). New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups. J. Cryptology 15(4):285–297. DOI: 10.1007/s00145-001-0018-3.
   Web of Science ®Google Scholar
• Miller, G. A. (1913). The product of two or more groups. Bull. Amer. Math. Soc. 19:303–310. DOI: 10.1090/S0002-9904-1913-02335-8.
   Google Scholar
• Rahimipour, A. R., Ashrafi, A. R., Gholami, A. (2018). The existence of minimal logarithmic signatures for some finite simple groups. Exp. Math. 27(2):138–146. DOI: 10.1080/10586458.2016.1235997.
   Web of Science ®Google Scholar
• Rahimipour, A. R. (2021). Exact factorizations of Sporadic simple groups. Exp. Math. 30:441–446. DOI: 10.1080/10586458.2018.1556137.
   Web of Science ®Google Scholar
• Szép, J. (1950). On the structure of groups which can be represented as the product of two subgroups. Acta Sci. Math. (Szeged) 12:57–61.
   Google Scholar
• Szép, J. On factorisable simple groups. Acta Sci. Math. (Szeged) 14:22.
   Google Scholar
• Zappa, G. (1942). Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili tra loro. (Italian), Atti Secondo Congresso Un. Mat. Ital., Bologna, 1940. Rome: Edizioni Cremonese, pp. 119–125.
   Google Scholar