پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,877 |
| تعداد مقالات | 15,278 |
| تعداد مشاهده مقاله | 43,732,108 |
| تعداد دریافت فایل اصل مقاله | 17,564,543 |
Locally finite p-groups with all subgroups either subnormal or nilpotent-by-Chernikov | ||
| International Journal of Group Theory | ||
| مقاله 6، دوره 1، شماره 1، خرداد 2012، صفحه 39-45 اصل مقاله (298.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2012.471 | ||
| نویسندگان | ||
| G. Cutolo* ؛ H. Smith | ||
| چکیده | ||
| We pursue further our investigation, begun in [H. Smith, Groups with all subgroups subnormal or nilpotent-by-Chernikov, Rend. Sem. Mat. Univ. Padova, 126 (2011), 245-253] and continued in [G. Cutolo and H. Smith, Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov. Centr. Eur. J. Math., (to appear)] of groups $G$ in which all subgroups are either subnormal or nilpotent-by-Chernikov. Denoting by $\mathfrak{X}$ the class of all such groups, our concern here is with locally finite p-groups in the class $\mathfrak{X}$, where $p$ is a prime, while an earlier article provided a reasonable classification of locally finite $\mathfrak{X}$ nb-groups in which all of the p-sections are nilpotent-by-Chernikov. Our main result is that if $G$ is a Baer p-group in $\mathfrak{X}$ then $G$ is nilpotent-by-Chernikov. | ||
| کلیدواژهها | ||
| locally finite groups؛ subnormal subgroups؛ nilpotent-by-Chernikov groups | ||
| مراجع | ||
|
A.O. Asar (2000) Locally nilpotent p-groups whose proper subgroups are
hypercentral or nilpotent-by-Chernikov J. London Math. Soc. (2) 61 (2), 412-422
C. Casolo (2002) On the structure of groups with all subgroups subnormal J. Group Theory 5 (3), 293-300
G. Cutolo and H. Smith Locally finite groups with all subgroups subnormal or nilpotent-by-Chernikov Centr. Eur. J. Math.
E. Detomi (2003) Groups with many subnormal subgroups J. Algebra 264 (2), 385-396
M.R. Dixon, M.J. Evans and H. Smith (2000) Groups with all proper subgroups nilpotent-by-finite rank Arch. Math. (Basel) 75 (2), 81-91
P. Hall (1958) Some sufficient conditions for a group to be nilpotent Illinois J. Math. 2, 787-801
W. Mohres (1989) Torsionsgruppen, deren Untergruppen alle subnormal sind Geom. Dedicata 31 (2), 237-244
W. Mohres (1990) Auflosbarkeit von Gruppen, deren Untergruppen alle
subnormal sind Arch. Math. (Basel) 54 (3), 232-235
F. Napolitani and E. Pegoraro (1997) On groups with nilpotent by Chernikov proper subgroups Arch. Math. (Basel) 69 (2), 89-94
H. Smith (1983) Hypercentral groups with all subgroups subnormal Bull. London Math. Soc. 15 (3), 229-234
H. Smith (2001) Groups with all non-nilpotent subgroups subnormal Topics in infinite groups, Quad. Mat. Dept. Math., Seconda Univ. Napoli, Caserta 8, 309-326
H. Smith (2001) On non-nilpotent groups with all subgroups subnormal Ricerche Mat. 50 (2), 217-221
H. Smith (2011) Groups with all subgroups subnormal or
nilpotent-by-Chernikov Rend. Sem. Mat. Univ. Padova 126, 245-253
H. Smith (2011) Groups that involve finitely many primes and have all subgroups subnormal J. Algebra 347 (1), 133-142
| ||
|
آمار تعداد مشاهده مقاله: 5,020 تعداد دریافت فایل اصل مقاله: 3,926 |
||