SOLVABILITY OF A NORMAL SUBGROUP IN RELATION TO ITS CHARACTER DEGREES
DOI:
https://doi.org/10.51406/jnset.v11i1.1413Keywords:
, Normal Subgroup, Character degrees, Solvable groups, Derived length and irreducible CharacterAbstract
In this work, how the structure of a normal subgroup of a group G is influenced by the degrees of an appropriate subset of irreducible character of a group G was verified. The characters that were used in controlling the structure of N Δ G are exactly those whose kernels do not contain N.
Given that N Δ G,
Irr (G/N) = {Є Irr (G)/N  ker }
and
cd (G/N) = { (1) / Â Â Irr (G/N)}
Â
References
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Isaacs I. M, 1975. ‘Character degrees and derived length of a solvable group Canada’ J. Math. 27: 146-151.
Isaacs I. M, Greg, K. 1998. ‘Irreducible Character Degrees and Normal subgroup Journal of Algebra 199: 302-326.
Isaacs I. M., Moreto, A. 2001. ‘The Character degrees and Nilpotence class of a p-group’ Journal of Algebra, 238, (16): 827-842
Jean P. S, 1977, ‘Linear Representations of finite group’ Springer Verlag.
Mark, L. L. 1998. ‘Derived Lengths and Character degrees’ Proceeding of the American Mathematical Society, (7): 1915-1921.
Berger T. R, 1976. `Characters and derived length in groups of odd order’ Journal of Algebra; 39, 199-207.
Berkovich, Y. G. 1989. ‘Degrees of Irreducible characters and normal P-complements’. Proceedings of American Mathematical Society, 106, 33-34.
Chen, S., Fan, Y., Shum, K. 2006. ‘Finite groups with character degrees of two distinct primes’ Wuhan University Journal of Natural Science II, (2), 343-345.
Cossey, J. P. 2007. ‘Bounds on the number of lifts of a Brauer Character in a P-solvable group’ Journal of Algebra, 312, 699-708.
Garrison S. C. 1973. ‘On Group with a small number of character Degrees’ Ph.D Thesis. University of Wisconsin, Madison (Unpublished)
Gluck, D. 1985, ‘Bounding the number of character degrees of a solvable groups Journal of London Mathematical Society, 2 (31): 457-462.
Gustavo A. F., Alexander, M. 2001. ‘Groups with two extreme Character degrees and their normal subgroups’ Transactions of the American Mathematical society 353, (6): 2171-2192.
Isaacs I. M, 1975. ‘Character degrees and derived length of a solvable group Canada’ J. Math. 27: 146-151.
Isaacs I. M, Greg, K. 1998. ‘Irreducible Character Degrees and Normal subgroup Journal of Algebra 199: 302-326.
Isaacs I. M., Moreto, A. 2001. ‘The Character degrees and Nilpotence class of a p-group’ Journal of Algebra, 238, (16): 827-842
Jean P. S, 1977, ‘Linear Representations of finite group’ Springer Verlag.
Mark, L. L. 1998. ‘Derived Lengths and Character degrees’ Proceeding of the American Mathematical Society, (7): 1915-1921.
