پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 43 |
| تعداد شماره‌ها | 1,706 |
| تعداد مقالات | 13,973 |
| تعداد مشاهده مقاله | 33,623,904 |
| تعداد دریافت فایل اصل مقاله | 13,337,051 |
Influence of complemented subgroups on the structure of finite groups | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 10، شماره 2، شهریور 2021، صفحه 65-74 اصل مقاله (206.89 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.119105.1570 | ||
| نویسنده | ||
| Izabela Agata Malinowska* | ||
| Faculty of Mathematics, University of Bialystok, 15-245 Bialystok, Ciolkowskiego 1M, Poland | ||
| چکیده | ||
| P. Hall proved that a finite group $G$ is supersoluble with elementary abelian Sylow subgroups if and only if every subgroup of $G$ is complemented in $G$. He called such groups complemented. A. Ballester-Bolinches and X. Guo established the structure of minimal non-complemented groups. We give the classification of finite non-soluble groups all of whose second maximal subgroups are complemented groups. We also prove that every finite group with less than $21$ non-complemented non-minimal $\{2,3,5\}$-subgroups is soluble. | ||
| کلیدواژه‌ها | ||
| Complemented subgroups؛ Complemented groups؛ Minimal non-complemented groups؛ Finite groups | ||
| مراجع | ||
|
[1] Z. Arad and E. Fisman, On finite factorizable groups, J. Algebra, 86 (1984) 522–548.
[2] A. Ballester-Bolinches, R. Esteban-Romero and D. J. S. Robinson, On finite minimal non-nilpotent groups, Proc. Amer. Math. Soc., 133 (2005) 3455–3462. [3] A. Ballester-Bolinches, R. Esteban-Romero and Lu Jiakuan, On finite groups with many supersoluble subgroups, Arch. Math. (Basel), 109 (2017) 3–8. [4] A. Ballester-Bolinches and X. Guo, On complemented subgroups of finite groups, Arch. Math. (Basel), 72 (1999) 161–166. [5] T. Connor and D. Leemans, An atlas of subgroup lattices of finite almost simple groups, arXiv:1306.4820., (2013) pp. 6. [6] L. E. Dickson, Linear groups. With an exposition of the Galois field theory, Dover Publications Inc, New York, 1958.
[7] X. Guo, K. P. Shum and A. Ballester-Bolinches, On complemented minimal subgroups in finite groups, J. Group Theory, 6 (2003) 159–167. [8] P. Hall, Complemented groups, J. London Math. Soc., 12 (1937) 201–204.
[9] B. Huppert, Endliche Gruppen I., Springer, Berlin, 1967.
[10] N. Ito, On the factorizations of the linear fractional group LF(2, pn), Acta Sci. Math. (Szeged), 15 (1953) 79–84.
[11] Y. Li, N. Su and Y. Wang, Complemented subgroups and the structure of finite groups, Monatsh. Math., 173 (2014) 361–370. [12] S. Li and Y. Zhao, Some finite nonsolvable groups characterized by their solvable subgroups, Acta Math. Sinica (N.S.), 4 (1988) 5–13. [13] V. S. Monakhov and V. N. Kniahina, On the Derived Length of a Finite Group with Complemented Subgroups of Order p2, Ukrainian Math. J., 67 (2015) 989–997. [14] J. S. Rose, A course on group theory., Cambridge University Press, Cambridge, (1978).
[15] M. Suzuki, A new type of simple groups of finite order, Proc. Nat. Acad. Sci. U. S. A., 46 (1960) 868–870. [16] M. Suzuki, Group theory I, Springer, Berlin, 1982. [17] J. G. Thompson, Nonsolvable finite groups all of whose local subgroups are solvable, Bull. Amer. Math. Soc., 74 (1968) 383–437. [18] R. A. Wilson, The finite simple groups, Springer–Verlag London Ltd., London, 2009. | ||
|
آمار تعداد مشاهده مقاله: 632 تعداد دریافت فایل اصل مقاله: 550 |
||