scholarly journals The computation of Schur multiplier and capability of pairs of groups of order p4

2020 ◽  
Author(s):  
Adnin Afifi Nawi ◽  
Nor Muhainiah Mohd Ali ◽  
Nor Haniza Sarmin
Keyword(s):  
Schur Multiplier

Some Inequalities for the Order of the Schur Multiplier of a Pair of Groups

2008 ◽  
Vol 36 (7) ◽  
pp. 2481-2486 ◽  
Author(s):  
Mohammad Reza R. Moghaddam ◽  
Ali Reza Salemkar ◽  
Taghi Karimi
Keyword(s):  
Schur Multiplier

Multiplicative Lie algebras and Schur multiplier

2019 ◽  
Vol 223 (9) ◽  
pp. 3695-3721 ◽  
Author(s):  
Ramji Lal ◽  
Sumit Kumar Upadhyay
Keyword(s):  
Lie Algebras ◽  
Schur Multiplier

On the schur multiplier ofp-groups

1999 ◽  
Vol 27 (9) ◽  
pp. 4173-4177 ◽  
Author(s):  
Graham Ellis
Keyword(s):  
Schur Multiplier

scholarly journals ON THE EXPONENT OF THE SCHUR MULTIPLIER OF A PAIR OF FINITE p-GROUPS

2013 ◽  
Vol 12 (08) ◽  
pp. 1350053
Author(s):  
FAHIMEH MOHAMMADZADEH ◽  
AZAM HOKMABADI ◽  
BEHROOZ MASHAYEKHY
Keyword(s):  
Upper Bound ◽  
Schur Multiplier

In this paper, we find an upper bound for the exponent of the Schur multiplier of a pair (G, N) of finite p-groups, when N admits a complement in G. As a consequence, we show that the exponent of the Schur multiplier of a pair (G, N) divides exp (N) if (G, N) is a pair of finite p-groups of class at most p – 1. We also prove that if N is powerfully embedded in G, then the exponent of the Schur multiplier of a pair (G, N) divides exp (N).

scholarly journals Computing the Nonabelian Tensor Square of Metacyclic p–Groups of Nilpotency Class Two

2013 ◽  
Vol 61 (1) ◽  
Author(s):  
A. M. Basri ◽  
N. H. Sarmin ◽  
N. M. Mohd Ali ◽  
J. R. Beuerle
Keyword(s):  
Commutator Subgroup ◽  
Group Structure ◽  
Nilpotency Class ◽  
Conjugacy Classes ◽  
Schur Multiplier ◽  
Group Order ◽  
Nonabelian Tensor ◽  
Current Article ◽  
Tensor Square ◽  
Compute Structure

In this paper, we develop appropriate programme using Groups, Algorithms and Programming (GAP) software enables performing different computations on various characteristics of all finite nonabelian metacyclic p–groups, p is prime, of nilpotency class 2. Such programme enables to compute structure of the group, order of the group, structure of the center, the number of conjugacy classes, structure of commutator subgroup, abelianization, Whitehead’s universal quadratic functor and other characteristics. In addition, structures of some other groups such as the nonabelian tensor square and various homological functors including Schur multiplier and exterior square can be computed using this programme. Furthermore, by computing the epicenter order or the exterior center order the capability can be determined. In our current article, we only compute the nonabelian tensor square of certain order groups, as an example, and give GAP codes for computing other characteristics and some subgroups.

scholarly journals The Schur multiplier of groups of order 𝑝5

2019 ◽  
Vol 22 (4) ◽  
pp. 647-687 ◽  
Author(s):  
Sumana Hatui ◽  
Vipul Kakkar ◽  
Manoj K. Yadav
Keyword(s):  
Schur Multiplier ◽  
Tensor Square ◽  
Exterior Square

AbstractIn this article, we compute the Schur multiplier, non-abelian tensor square and exterior square of non-abelian p-groups of order {p^{5}}. As an application, we determine the capability of groups of order {p^{5}}.

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