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Research Article

On a criterion for solvability of a finite group

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Pages 2234-2240 | Received 27 Sep 2020, Accepted 08 Dec 2020, Published online: 10 Jan 2021

References

  • Amiri, H., Jafarian Amiri, S. M., Isaacs, I. M. (2009). Sums of element orders in finite groups. Commun. Algebra 37(9):2978–2980. DOI: 10.1080/00927870802502530.
  • Amiri, H., Jafarian Amiri, S.M. (2011). Sum of element orders on finite groups of the same order. J. Algebra Appl. 10(02):187–190. DOI: 10.1142/S0219498811004057.
  • Amiri, H., Jafarian Amiri, S.M. (2012). Sums of element orders of maximal subgroups of the symmetric group. Commun. Algebra 40(2):770–778. DOI: 10.1080/00927872.2010.537290.
  • Belonogov, V.A. (1988). Finite groups with three classes of maximal subgroups. Math. USSR. Sb. 59(1):223–236. DOI: 10.1070/SM1988v059n01ABEH003132.
  • Brandl, R., Wujie, S. (1994). The characterization of PSL(2, q) by its element orders. J. Algebra 163(1):109–114. DOI: 10.1006/jabr.1994.1006.
  • De Medts, T., Tărnăuceanu, M. (2008). Finite groups determined by an inequality of the order of their subgroups. Bull. Belg. Math. Soc. Simon Stevin. 15(4):699–704. DOI: 10.36045/bbms/1225893949.
  • Di Domenico, E., Monetta, C., Noce, M. (2022). On the product of element orders of a finite group, to appear.
  • Garonzi, M., Patassini, M. (2017). Inequalities detecting structural properties of a finite group. Commun. Algebra 45(2):677–687. DOI: 10.1080/00927872.2016.1172621.
  • Herstein, I.N. (1958). A remark on finite groups. Proc. Amer. Math. Soc. 9(2):255–257. DOI: 10.1090/S0002-9939-1958-0093542-8.
  • Herzog, M., Longobardi, P., Maj, M. Sums of element orders in groups of odd order. arXiv:1901.09662.
  • Herzog, M., Longobardi, P., Maj, M. (2021). The second maximal groups with respect to the sums of element orders. J. Pure Appl. Algebra 225(3):106531. DOI: 10.1016/j.jpaa.2020.106531.
  • Herzog, M., Longobardi, P., Maj, M. (2018). An exact upper bound for sums of elements order in non-cyclic finite groups. J. Pure Appl. Algebra 222(7):1628–1642. DOI: 10.1016/j.jpaa.2017.07.015.
  • Herzog, M., Longobardi, P., Maj, M. (2018). Properties of finite and periodic groups determined by their elements orders (a survey). In: Sastry N., Yadav M., eds. Group Theory and Computation. Indian Statistical Institute Series. Singapore: Springer, pp. 59–90.
  • Herzog, M., Longobardi, P., Maj, M. (2019). Sums of element orders in groups of order 2m with m odd. Commun. Algebra 47(5):2035–2048. DOI: 10.1080/00927872.2018.1527924.
  • Herzog, M., Longobardi, P., Maj, M. (2018). Two criteria for solvability of finite groups. J. Algebra 511:215–226. DOI: 10.1016/j.jalgebra.2018.06.015.
  • Huppert, B. (1967). Endliche Gruppen. Berlin: Springer-Verlag.
  • Jafarian Amiri, S.M. (2013). Second maximal sum of element orders in finite nilpotent groups. Commun. Algebra 41(6):2055–2059. DOI: 10.1080/00927872.2011.653070.
  • Jafarian Amiri, S.M. (2013). Maximal sum of element orders of all proper subgroups of PGL(2, q). Bull. Iran. Math. Soc. 39(3):501–505.
  • Jafarian Amiri, S.M. (2013). Characterization of A5 and PSL(2, 7) by sum of element orders. Int. J. Group Theory 2(2):35–39.
  • Jafarian Amiri, S.M., Amiri, M. (2014). Second maximal sum of element orders in finite groups. J. Pure Appl. Algebra 218(3):531–539. DOI: 10.1016/j.jpaa.2013.07.003.
  • Jafarian Amiri, S.M., Amiri, M. (2014). Sum of the products of the orders of two distinct elements in finite groups. Commun. Algebra 42(12):5319–5328. DOI: 10.1080/00927872.2013.839697.
  • Jafarian Amiri, S.M., Amiri, M. (2015). Characterization of p-groups by sum of the element orders. Publ. Math. Debrecen. 86(1-2):31–37. DOI: 10.5486/PMD.2015.5961.
  • Jafarian Amiri, S.M., Amiri, M. (2017). Sum of element orders in groups with square-free orders. Bull. Malays. Math. Sci. Soc. 40(3):1025–1034. DOI: 10.1007/s40840-016-0353-z.
  • Marefat, Y., Iranmanesh, A., Tehranian, A. (2013). On the sum of element orders of finite simple groups. J. Algebra Appl. 12(07):1350026. DOI: 10.1142/S0219498813500266.
  • Shen, R., Chen, G., Wu, C. (2015). On groups with the second largest value of the sum of element orders. Commun. Algebra 43(6):2618–2631. DOI: 10.1080/00927872.2014.900686.
  • Suzuki, M. (1986). Group Theory II. Berlin: Springer-Verlag.
  • Tărnăuceanu, M., Fodor, D.G. (2014). On the sum of element orders of finite abelian groups. Sci. An. Univ.” A1.I. Cuza” Iasi, Ser. Math. 60(1):1–7. DOI: 10.2478/aicu-2013-0013.
  • Tărnăuceanu, M. (2013). A note on the product of element orders of finite abelian groups. Bull. Malays. Math. Sci. Soc. 36:1123–1126.
  • Tărnăuceanu, M. (2017). Finite groups determined by an inequality of the order of their subgroups II. Commun. Algebra 45(11):4865–4868. DOI: 10.1080/00927872.2017.1284228.
  • Tărnăuceanu, M. A criterion for solvability of a finite group by the sum of subgroup orders. arXiv:1907.02185, 1907.02185v2.

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