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Variations on Glauberman's ZJ theorem | ||
| International Journal of Group Theory | ||
| دوره 11، شماره 2، شهریور 2022، صفحه 43-52 اصل مقاله (309.04 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2021.126329.1659 | ||
| نویسنده | ||
| Daniel Allcock* | ||
| Department of Mathematics, University of Texas at Austin, RLM 8.100, 2515 Speedway Stop C1200, Austin, Texas, USA 78712-1202 | ||
| چکیده | ||
| We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group~$S$, that contain ZJr(S) and ZJo(S) respectively and can be strictly larger. | ||
| کلیدواژهها | ||
| Thompson subgroup؛ Glauberman Replacement؛ ZJ Theorem | ||
| مراجع | ||
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[1] S. Gagola, Unpublished course notes, Year(s) unknown.
[2] G. Glauberman, A characteristic subgroup of a p-stable group, Canad. J. Math., 20 (1968) 1101–1135.
[3] G. Glauberman and R. Solomon, A new characteristic subgroup of a p-stable group, J. Algebra, 368 (2012) 231–236.
[4] D. Gorenstein, Finite Groups (2nd ed.), AMS Chelsea Publishers, Providence RI (USA), 2007.
[5] I. M. Isaacs, An alternative proof of the Thompson replacement theorem. J. Algebra, 15 (1970) 149–150.
[6] M. yasir Kızmaz, An extension of the Glauberman ZJ-theorem, Int. J. Algebra and Comput., 31 (2021) 117–133.
[7] H. Kurzweil and B. Stellmacher, The Theory of Finite Groups: an Introduction, Springer-Verlag, New York, N.Y. (USA), 2004. [8] Stellmacher, B., An analogue to Glauberman’s ZJ-theorem, Proc. Amer. Math. Soc., 109 (1990) 925–929. Errata in Proc. Amer. Math. Soc., 114 (1992) 588. | ||
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