Computing the Nonabelian Tensor Square of Metacyclic p–Groups of Nilpotency Class Two
DOI:
https://doi.org/10.11113/jt.v61.1619Keywords:
p–Groups, Metacyclic groups, groups, algorithms and programmingAbstract
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.References
[1] H-S Sim. 1994. Metacyclic Groups of Odd Order, Proc. London Math.
Soc. 3(69): 47–71.
C. E. Hempel. 2000. Metacyclic Groups, Bull. Austral. Math. Soc. 61:
–524.
J. B. Fraleigh. 1982. First Course In Abstract Algebra. Addison
Wesley, USA.
J. Beuerle. 2005. An Elementary Classification of Finite Metacyclic p-
Groups of Class at Least Three. Algebra Colloquium. Soc. 43. 553–
R. Brown, D. L. Johnson and E. F. Robertson. 1987. Some
Computations of Nonabelian Tensor Products of Groups. J. Algebra.
177–202.
J. G. Rainbolt, J. A. Gallian. 2010. Abstract Algebra With GAP.
Books/Cole, Cengage Learning, Boston.
D. J. S. Robinson. 1993. A Course in the Theory of Groups. Springer-
Verlag, Berlin.
M. Bacon, L-C Kappe. 1993. The Nonabelian Tensor Square of A 2-
generator p-groups of Class 2. Arch. Math. 61: 508–516.
L-C Kappe, N. Sarmin and M. Visscher.1999. Two-Generator 2-
groups of Class 2 and Their Nonabelian Tensor Squares. Glasgow
Math. J. 41: 417–430.
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