On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups

N. Shajareh Poursalavati

doi:doi:10.11648/j.pamj.20140301.12

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On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups

N. Shajareh Poursalavati

Published in Pure and Applied Mathematics Journal (Volume 3, Issue 1)

Received: 25 January 2014 Published: 20 February 2014

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Abstract

In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.

Published in	Pure and Applied Mathematics Journal (Volume 3, Issue 1)
DOI	10.11648/j.pamj.20140301.12
Page(s)	7-10
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Symmetry Classes of Tensors, Frobenius Groups

References

[1]	M.R. Darafsheh, N.S. Poursalavati, Orthogonal basis of the symmetry classes of tensors as¬sociated with the direct product of permutation groups, Pure Mathematics and Applicans, 10 (1999), pp. 241–248.
[2]	M.R. Darafsheh, N.S. Poursalavati, On the existence of the orthogonal basis of the symmetry classes of tensors associated with certain groups, SUT Journal of Mathematics, 37 (2001), pp. 1–17.
[3]	R. Freese, Inequalities for generalized matrix functions based on arbitrary characters, Linear Algebra, 7 (1973), pp. 337–345.
[4]	R.R. Holmes, Orthogonal bases of symmetrized tensor spaces, Linear and Multilinear Algebra, 39 (1995), pp. 241–243.
[5]	G. James, M. Liebeck, Representations and characters of groups, Cambridge University Press, 1993.
[6]	M. Marcus, Finite Dimensional Multilinear Algebra, part I, Marcel Dekker, 1973.
[7]	R. Merris, Multilinear Algebra, Gordon and Breach science publishers, 1997.
[8]	N. Shajareh Poursalavati, On the symmetry classes of tensors associated with certain Frobenius groups, the 43rd Annual Iranian Mathematics Conference, 27-30 August 2012, University of Tabriz, Tabriz, Iran, (2012), pp 149-152.
[9]	B.Y. Wang, M.P. Gonge, The subspace and orthonormal bases of symmetry classes of tensors, Linear and Multilinear Algebra, 30 (1991), pp. 195–204.

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APA Style

N. Shajareh Poursalavati. (2014). On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure and Applied Mathematics Journal, 3(1), 7-10. https://doi.org/10.11648/j.pamj.20140301.12

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ACS Style

N. Shajareh Poursalavati. On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure Appl. Math. J. 2014, 3(1), 7-10. doi: 10.11648/j.pamj.20140301.12

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AMA Style

N. Shajareh Poursalavati. On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure Appl Math J. 2014;3(1):7-10. doi: 10.11648/j.pamj.20140301.12

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@article{10.11648/j.pamj.20140301.12,
  author = {N. Shajareh Poursalavati},
  title = {On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {1},
  pages = {7-10},
  doi = {10.11648/j.pamj.20140301.12},
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  abstract = {In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.},
 year = {2014}
}

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T1  - On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups
AU  - N. Shajareh Poursalavati
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PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140301.12
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JF  - Pure and Applied Mathematics Journal
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Author Information

N. Shajareh Poursalavati

Dept. of Mathematics and Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

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APA Style

N. Shajareh Poursalavati. (2014). On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure and Applied Mathematics Journal, 3(1), 7-10. https://doi.org/10.11648/j.pamj.20140301.12

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ACS Style

N. Shajareh Poursalavati. On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure Appl. Math. J. 2014, 3(1), 7-10. doi: 10.11648/j.pamj.20140301.12

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AMA Style

N. Shajareh Poursalavati. On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups. Pure Appl Math J. 2014;3(1):7-10. doi: 10.11648/j.pamj.20140301.12

Copy | Download

@article{10.11648/j.pamj.20140301.12,
  author = {N. Shajareh Poursalavati},
  title = {On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups},
  journal = {Pure and Applied Mathematics Journal},
  volume = {3},
  number = {1},
  pages = {7-10},
  doi = {10.11648/j.pamj.20140301.12},
  url = {https://doi.org/10.11648/j.pamj.20140301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20140301.12},
  abstract = {In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - On the Symmetry Classes of Tensors Associated with Certain Frobenius Groups
AU  - N. Shajareh Poursalavati
Y1  - 2014/02/20
PY  - 2014
N1  - https://doi.org/10.11648/j.pamj.20140301.12
DO  - 10.11648/j.pamj.20140301.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 7
EP  - 10
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20140301.12
AB  - In this paper, we study the symmetry classes of tensors associated with some Frobenius groups of order pq, where q|p-1as a subgroups of the full symmetric group on p letters. We calculate the dimension of the symmetry classes of tensor associated with some Frobenius groups and some irreducible complex characters and we obtain two useful corollary with an example.
VL  - 3
IS  - 1
ER  -

Copy | Download