پیوندهای مفید
اخبار و اعلانات
آمار
| تعداد نشریات | 44 |
| تعداد شمارهها | 1,877 |
| تعداد مقالات | 15,278 |
| تعداد مشاهده مقاله | 43,731,910 |
| تعداد دریافت فایل اصل مقاله | 17,564,255 |
Groups of order p8 and exponent p | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 4، شماره 4، اسفند 2015، صفحه 25-42 اصل مقاله (224.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2015.5758 | ||
| نویسنده | ||
| Michael Vaughan-Lee* | ||
| Oxford University Mathematical Institute | ||
| چکیده | ||
| We prove that for $p>7$ there are \[ p^{4}+2p^{3}+20p^{2}+147p+(3p+29)\gcd (p-1,3)+5\gcd (p-1,4)+1246 \] groups of order $p^{8}$ with exponent $p$. If $P$ is a group of order $p^{8}$ and exponent $p$, and if $P$ has class $c>1$ then $P$ is a descendant of $ P/\gamma _{c}(P)$. For each group of exponent $p$ with order less than $ p^{8} $ we calculate the number of descendants of order $p^{8}$ with exponent $p$. In all but one case we are able to obtain a complete and irredundant list of the descendants. But in the case of the three generator class two group of order $p^{6}$ and exponent $p$ ($p>3$), while we are able to calculate the number of descendants of order $p^{8}$, we have not been able to obtain a list of the descendants. | ||
| کلیدواژهها | ||
| Groups of exponent $p$؛ Groups of order $p^8$؛ PORC conjecture | ||
| مراجع | ||
|
G. Bagnera (1898) La composizione dei gruppi finiti il cui grado e la quinta
potenza di un numero primo Ann. Mat. Pura Appl. 3 (1), 137-228
H. R. Brahana (1951) Finite metabelian groups and the lines of a projective four-space Amer. J. Math. 73, 539-555
J. Cannon, W. Bosma and C. Playoust (1997) The Magma algebra system I: The user language J. Symbolic Comput. 24, 235-265
F. N. Cole and J. W. Glover (1893) On groups whose orders are products of three prime factors Amer. J. Math. 15, 191-220
A. Cop etti (2005) Finite-dimensional Lie algebras of nilpotency class 2 Masters Thesis, Australian National University
M. du Sautoy and M. Vaughan-Lee (2012) Non-PORC behaviour of a class of descendant p-groups J. Algebra 361, 287-312
B. Eick, H. U. Besche and E. A. O'Brien (2001) The groups of order at most 2000 Electron. Res. Announc. Amer. Math. Soc. 7, 1-4
A. Evseev (2008) Higman's PORC conjecture for a family of groups Bul l. Lond. Math. Soc. 40, 415-431
The GAP Group (2014) GAP-Groups, Algorithms, and Programming, Version 4.7.5 http://www.gap- system.org
G. Higman (1960) Enumerating p-groups. I: Inequalities Proc. London Math. Soc. (3) 10, 24-30
G. Higman (1960) Enumerating p -groups. II: Problems whose solution is PORC Proc. London Math. Soc. (3) 10, 566-582
O. Holder (1893) Die Grupp en der Ordnungen p^3, pq^2, pq^r, p^4 Math. Ann. 43, 301-412
E. Netto (1882) Substitutionentheorie und ihre Anwendungen auf die Algebra Teubner, Leipzig
M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee (2004) Groups and nilpotent Lie rings whose order is the sixth
power of a prime J. Algebra 278, 383-401
E. A. O'Brien (1990) The p-group generation algorithm J. Symbolic Comput. 9, 677-698
E. A. O'Brien (1991) The groups of order 256 J. Algebra 143, 219-235
E. A. O'Brien and M. R. Vaughan-Lee (2005) The groups with order p^7 for odd prime p J. Algebra 292, 243-258
M. Vaughan-Lee (2012) On Graham Higman's famous PORC paper Int. J. Group Theory 1 (4), 65-79
M. Vaughan-Lee and B. Eick (2013) LiePRing - a GAP package Version 1.5, http://www.gap- system.org/
Packages/liepring.html
J. W. A. Young (1893) On the determination of groups whose order is a power of a prime Amer. J. Math. 15, 124-178
| ||
|
آمار تعداد مشاهده مقاله: 4,538 تعداد دریافت فایل اصل مقاله: 3,309 |
||