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Mohammadzadeh, Fahimeh, Hokmabadi, Azam, Mashayekhy, Behrooz. (1392). On the order of the Schur multiplier of a pair of finite p-groups II. , 2(3), 1-8. doi: 10.22108/ijgt.2013.2007
Fahimeh Mohammadzadeh; Azam Hokmabadi; Behrooz Mashayekhy. "On the order of the Schur multiplier of a pair of finite p-groups II". , 2, 3, 1392, 1-8. doi: 10.22108/ijgt.2013.2007
Mohammadzadeh, Fahimeh, Hokmabadi, Azam, Mashayekhy, Behrooz. (1392). 'On the order of the Schur multiplier of a pair of finite p-groups II', , 2(3), pp. 1-8. doi: 10.22108/ijgt.2013.2007
Mohammadzadeh, Fahimeh, Hokmabadi, Azam, Mashayekhy, Behrooz. On the order of the Schur multiplier of a pair of finite p-groups II. , 1392; 2(3): 1-8. doi: 10.22108/ijgt.2013.2007

On the order of the Schur multiplier of a pair of finite p-groups II

International Journal of Group Theory
مقاله 1، دوره 2، شماره 3، آذر 2013، صفحه 1-8    اصل مقاله (405.52 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2013.2007
نویسندگان
Fahimeh Mohammadzadeh1؛ Azam Hokmabadi* 1؛ Behrooz Mashayekhy2
1Payame Noor University of Iran
2Ferdowsi University of Mashhad
چکیده
‎Let $G$ be a finite $p$-group and $N$ be a normal subgroup of $G$ with‎ ‎$|N|=p^n$ and $|G/N|=p^m$‎. ‎A result of Ellis (1998) shows‎ ‎that the order of the Schur multiplier of such a pair $(G,N)$ of finite $p$-groups is bounded‎ ‎by $ p^{\frac{1}{2}n(2m+n-1)}$ and hence it is equal to $‎ ‎p^{\frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$‎. ‎Recently‎, ‎the authors have characterized the structure of $(G,N)$ when $N$ has a complement in $G$ and‎ ‎$t\leq 3$‎. ‎This paper is devoted to classification of pairs‎ ‎$(G,N)$ when $N$ has a normal complement in $G$ and $t=4,5$‎.
کلیدواژه‌ها
Pair of groups؛ Schur multiplier؛ finite $p$-groups
مراجع
Ya. G. Berkovich (1991) On the order of the commutator subgroup and Schur multiplier of a finite p-group J. Algebra 144, 269-272
G. Ellis (1998) The Schur multiplier of a pair of groups Appl. Categ. Structures 6, 355-371
G. Ellis (1999) On the Schur multiplier of p-groups Comm. Algebra 27 (9), 4173-4177
J. A. Green (1956) On the number of outomorphisms of a finite p-group Proc. Roy. Soc. London Ser. A 237, 574-581
A. Hokmabadi, F. Mohammadzadeh and B. Mashayekhy On the order of the Schur multiplier of a pair of finite $p$-groups arxive: 1101.2503v2
G. Karpilovsky (1987) The Schur Multiplier Clarendon Press, Oxford
P. Niroomand Characterizing finite $p$-groups by their Schur multipliers arXiv: 1001.4256v1
P. Niroomand Characterizing finite $p$-groups by their Schur multipliers $t(G)=5$ arXiv: 1001.4257v1
A. R. Salemkar, M. R. R. Moghaddam, M. Davarpanah and F. Saeedi (2007) A remark on the Schur multiplier of $p$-groups Comm. Algebra 35, 1215-1221
A. R. Salemkar, M. R. Moghaddam and F. Saeedi (2006) The commutator subgroup and Schur multiplier of finite $p$-groups J. Aust. Math. Soc. 81, 1-9
X. Zhou (1994) On the order of Schur multipliers of finite $p$-groups Comm. Algebra 22 (1), 1-8
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