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Dixon, Martyn, Evans, Martin, Smith, Howard. (1391). Omissible extensions of SL2(k) where k is a field of positive characteristic. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 2(1), 145-155. doi: 10.22108/ijgt.2013.2739
Martyn Dixon; Martin Evans; Howard Smith. "Omissible extensions of SL2(k) where k is a field of positive characteristic". سامانه مدیریت نشریات علمی دانشگاه اصفهان, 2, 1, 1391, 145-155. doi: 10.22108/ijgt.2013.2739
Dixon, Martyn, Evans, Martin, Smith, Howard. (1391). 'Omissible extensions of SL2(k) where k is a field of positive characteristic', سامانه مدیریت نشریات علمی دانشگاه اصفهان, 2(1), pp. 145-155. doi: 10.22108/ijgt.2013.2739
Dixon, Martyn, Evans, Martin, Smith, Howard. Omissible extensions of SL2(k) where k is a field of positive characteristic. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 1391; 2(1): 145-155. doi: 10.22108/ijgt.2013.2739

Omissible extensions of SL2(k) where k is a field of positive characteristic

International Journal of Group Theory
مقاله 12، دوره 2، شماره 1، خرداد 2013، صفحه 145-155    اصل مقاله (463.62 K)
نوع مقاله: Ischia Group Theory 2012
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2739
نویسندگان
Martyn Dixon1؛ Martin Evans* 1؛ Howard Smith2
1The University of Alabama
2Bucknell University
چکیده
A normal subgroup $N$ of a group $G$ is said to be an‎ omissible subgroup of $G$ if it has the following property‎: ‎whenever $X\leq G$ is such that $G=XN$‎, ‎then $G=X$‎. ‎In this note we construct various groups $G$‎, ‎each of which has an omissible subgroup $N\neq 1$ such that $G/N\cong SL_2(k)$ where $k$ is a field of positive characteristic‎.
کلیدواژه‌ها
Omissible subgroup؛ special linear group؛ Frattini extension؛ locally (soluble-by-finite) group
مراجع
J. V. Brawley and G. E. Schnibben (1989) Infinite Agebraic Extensions of Finite Fields Contemporary Mathematics, American Math. Soc., Providence, RI. 95
Contemporary Mathematics, American Math. Soc., Providence, RI. (2000) Topics in Geometric Group Theory Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL
M. R. Dixon and M. J. Evans (1999) Groups with the minimum condition on insoluble subgroups Arch. Math. (Basel) 72, 241-251
M. R. Dixon, M. J. Evans and H. Smith (2005) Groups with all proper subgroups soluble-by-finite rank J. Algebra 289, 135-147
S. D. Kozlov (1991) Frattini extensions of the projective special linear group Sibirsk. Math. Zh., 32 no. 2 (1991) 88--93. English translation in: Siberian Math. J. 32 (2), 252-256
H. Matsumura (1989) Commutative Ring Theory Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge 8
D. J. S. Robinson (1996) A course in the theory of groups Graduate Texts in Mathematics, Springer Verlag, Berlin, Heidelberg, New York 80
J-P. Serre (1968) Abelian $\ell$-adic Representations and Elliptic Curves W. A. Benjamin, Inc., New York-Amsterdam
J-P. Serre (1979) Local Fields Graduate Texts in Mathematics, Springer-Verlag, New York, Berlin 67
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