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On a result of nilpotent subgroups of solvable groups | ||
International Journal of Group Theory | ||
مقاله 4، دوره 11، شماره 3، آذر 2022، صفحه 187-189 اصل مقاله (301.34 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22108/ijgt.2021.128455.1690 | ||
نویسنده | ||
Yong Yang* | ||
Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, USA | ||
چکیده | ||
Heineken [H. Heineken, Nilpotent subgroups of finite soluble groups, Arch. Math.(Basel), 56 no. 5 (1991) 417--423.] studied the order of the nilpotent subgroups of the largest order of a solvable group. We point out an error, and thus refute the proof of the main result of [H. Heineken, Nilpotent subgroups of finite soluble groups, Arch. Math.(Basel)}, 56 no. 5 (1991) 417--423]. | ||
کلیدواژهها | ||
solvable group؛ nilpotent group؛ injector | ||
مراجع | ||
[1] J. Cossey, Z. Halasi, A. Maróti and H. N. Nguyen, On a conjecture of Gluck, Math. Z.,279 no. 3-4 (2015) 1067–1080.
[2] H. Heineken, Nilpotent subgroups of finite soluble groups, Arch. Math.(Basel), 56 no. 5 (1991) 417–423.
[3] M. Liebeck and L. Pyber, Upper bounds for the number of conjugacy classes of a finite group, J. Algebra, 198 no. 2 (1997) 538–562. [4] L. Pyber, How abelian is a finite group? The mathematics of Paul Erdös, I, Algorithms Combin., 13, Springer, Berlin, 1997 372–384. | ||
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