The Exterior Squares of Some Crystallographic Groups
DOI:
https://doi.org/10.11113/jt.v62.1882Keywords:
Crystallographic groups, Bieberbach groups, exterior squaresAbstract
A crystallographic group is a discrete subgroup G of the set of isometries of Euclidean space En, where the quotient space En/G is compact. A specific type of crystallographic groups is called Bieberbach groups. A Bieberbach group is defined to be a torsion free crystallographic group. In this paper, the exterior squares of some Bieberbach groups with abelian point groups are computed. The exterior square of a group is the factor group of the nonabelian tensor square with the central subgroup of the group.References
D. R. Farkas. 1981. Rocky Mountain Journal of Mathematics. 11(4): 511.
H. Hiller. 1986. The American Mathematical Monthly. 93(10): 765.
W. Plesken, T. Schulz. 2000. Experimental Mathematics. 9 (3): 407.
C. Cid, T. Schulz. 2001. Experimental Mathematics. 10(1): 109.
Rohaidah Masri. 2009. Ph.D. Thesis, Universiti Teknologi Malaysia.
R. Brown, J. L. Loday. 1987. Topology. 26(3): 311.
L. C. Kappe, M. P. Visscher, N. H. Sarmin. 1999. Glasgow Mathematical Journal. 41(3): 417.
J. R. Beuerle, L. C. Kappe. 2000. Proc. Edinburgh Math. Soc. (2). 43(3): 651.
R. D. Blyth, P. Moravec, R. F. Morse. 2008. Contemporary Mathematics. 470: 27.
M. R. Bacon, L. C. Kappe. 2003. Illinois Journal of Math. 47: 49.
N. M. Mohd Ali, N. H. Sarmin, L. C. Kappe. 2007. Proceeding of 15th Mathematical Sciences National Conference (SKSM 15). 71–76.
V. A. R. Ramachandran, N. H. Sarmin, N. M. Mohd Ali. 2008. Proceeding of Regional Annual Fundamental Science Seminar. 350–354.
B. Eick, W. Nickel. 2008. Journal of Algebra. 320: 927.
N. R. Rocco. 1991. Soc. Brasil. Mat. (N. S.). 22(1): 63.
G. Ellis, F. Leonard. 1995. Proc. Roy. Irish Acad Sect. A. 95(2): 137.
R. D. Blyth, R. F. Morse. 2009. Journal of Algebra. 321: 2139.
R. D. Blyth, F. Fumagalli, M. Morigi. 2010. J. Group Theory. 13: 83.
R. Brown, D. L. Johnson, E. F. Robertson. 1987. Journal of Algebra. 111: 177.
A. J. Zomorodian. 2005. Topology for Computing. New York: Cambridge University Press.
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