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On infinite groups whose finite quotients have restricted prime divisors | ||
| International Journal of Group Theory | ||
| مقاله 9، دوره 10، شماره 2، شهریور 2021، صفحه 75-88 اصل مقاله (237.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2020.119054.1569 | ||
| نویسنده | ||
| Derek J. S. Robinson* | ||
| Department of Mathematics, University of Illinois at Urbana-Champaign Urbana, IL, 61801, USA. | ||
| چکیده | ||
| The effect of restricting the set of primes dividing the orders of the finite quotients of a group is investigated. Particular attention is paid to abelian, soluble, locally soluble and locally finite groups. The connection with the extraction of roots is explored. | ||
| کلیدواژه‌ها | ||
| Finite quotients؛ Prime divisors | ||
| مراجع | ||
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[1] G. Baumslag, Some aspects of groups with unique roots, Acta Math., 104 (1960) 217–303.
[2] V. V. Belyaev, Locally finite groups with Cernikov Sylow p-subgroups, Algebra i Logika, 20 (1981) 605–619.
[3] V. S. Carin, On groups of automorphisms of nilpotent groups, Ukrain. Mat. Z., 6 (1954) 295–304.
[4] S. N. Cernikov, Complete groups possessing ascending central series, Mat. Sb., 18 (1946) 397–421.
[5] S. N. Cernikov, On the theory of complete groups, Mat. Sbornik N. S., 22 (1948) 319–348, English transl, Amer. Math. Soc., Translations 1(56) (1951) 3–49. [6] M. R. Dixon, Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, Series in Algebra, 2, World Scientific Publishing Co., Singapore 1994. [7] S. Friedenberg and P. Wolf, A brief journey through extensions of rational groups, Rend. Sem. Mat. Univ. Padova, 140 (2018) 123–128. [8] L. Fuchs, Infinite Abelian Groups, vol. 2, Academic Press, New York, NY, 1970-73.
[9] J. C. Lennox and D. J. S. Robinson, The Theory of Infinite Soluble Groups, Clarendon Press, Oxford, 2004.
[10] D. J. S. Robinson, Finiteness Conditions and Generalized Soluble Groups, vol. 2, Springer Verlag, Berlin, 1972. | ||
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آمار تعداد مشاهده مقاله: 264 تعداد دریافت فایل اصل مقاله: 383 |
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