Total Character of a Group G with (G, Z(G)) as a Generalized Camina Pair
Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 392-402

Voir la notice de l'article provenant de la source Cambridge University Press

We investigate whether the total character of a finite group $G$ is a polynomial in a suitable irreducible character of $G$ . When $\left( G,\,Z\left( G \right) \right)$ is a generalized Camina pair, we show that the total character is a polynomial in a faithful irreducible character of $G$ if and only if $Z\left( G \right)$ is cyclic.
DOI : 10.4153/CMB-2015-074-5
Mots-clés : 20C15, finite groups, group characters, total characters
Prajapati, S. K.; Sarma, R. Total Character of a Group G with (G, Z(G)) as a Generalized Camina Pair. Canadian mathematical bulletin, Tome 59 (2016) no. 2, pp. 392-402. doi: 10.4153/CMB-2015-074-5
@article{10_4153_CMB_2015_074_5,
     author = {Prajapati, S. K. and Sarma, R.},
     title = {Total {Character} of a {Group} {G} with {(G,} {Z(G))} as a {Generalized} {Camina} {Pair}},
     journal = {Canadian mathematical bulletin},
     pages = {392--402},
     year = {2016},
     volume = {59},
     number = {2},
     doi = {10.4153/CMB-2015-074-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-074-5/}
}
TY  - JOUR
AU  - Prajapati, S. K.
AU  - Sarma, R.
TI  - Total Character of a Group G with (G, Z(G)) as a Generalized Camina Pair
JO  - Canadian mathematical bulletin
PY  - 2016
SP  - 392
EP  - 402
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-074-5/
DO  - 10.4153/CMB-2015-074-5
ID  - 10_4153_CMB_2015_074_5
ER  - 
%0 Journal Article
%A Prajapati, S. K.
%A Sarma, R.
%T Total Character of a Group G with (G, Z(G)) as a Generalized Camina Pair
%J Canadian mathematical bulletin
%D 2016
%P 392-402
%V 59
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2015-074-5/
%R 10.4153/CMB-2015-074-5
%F 10_4153_CMB_2015_074_5

[1] [1] Berkovich, Y., Groups of prime power order. Vol. 1, de Gruyter Expositions in Mathematics 46, Walter de Gruyter, Berlin, 2008. Google Scholar

[2] [2] Gagola, S. M., Jr. and Lewis, M. L., Squares of characters that are the sum of all irreducible characters. Illinois J. Math. 42(1998), no. 4, 655–672. Google Scholar

[3] [3] Gow, R., Properties of the finite linear group related to the transpose-inverse involution. Proc. London Math. Soc. 47(1983), no. 3, 493–506. Google Scholar | DOI

[4] [4] Heffernan, R. and MacHale, D., On the sum of the character degrees of a finite group. Math.Proc. R. Ir. Acad. 108(2008), no. 1, 57–63. Google Scholar | DOI

[5] [5] Isaacs, I. M., Character theory of finite groups. Pure and Applied Mathematics 69. Academic Press, New York, 2000 Google Scholar

[6] [6] Isaacs, I. M., Loukaki, M., and Moreto, A., The average degree of an irreducible character of a finite group. Israel J. Math. 197(2013), no. 1, 55–67. Google Scholar | DOI

[7] [7] James, G. and Liebeck, M., Representations and characters of groups.Second edition. Cambridge University Press, New York, 2001. Google Scholar

[8] [8] Karpilovsky, G., Group representations. Vol. 1. Part B, In: Introduction to group representations and characters. North-Holland Mathematics Studies, 175.North-Holland, Amsterdam, 1992, pp. i–xiv, 621–1274. Google Scholar

[9] [9] Kodiyalam, V. and Verma, D. N., A natural representation model for symmetric groups. arxiv:math/0402216. Google Scholar

[10] [10] Lemieux, S., Finite exceptional p-groups of small order. Comm. Algebra 35(2007), no. 6, 1890–1894. Google Scholar | DOI

[11] [11] Lewis, M. L., Character tables of groups where all nonlinear irreducible characters vanish off the center. In: Ischia group theory 2008. World Sci. Publ. Hackensack, NJ, 2009, pp. 174–182. Google Scholar | DOI

[12] [12] Lewis, M. L., The vanishing-off subgroup. J. Algebra 321(2009), no. 4,1313-1325. Google Scholar | DOI

[13] [13] Magaard, K., and Tong-Viet, H. P., Character degree sums infinite nonsolvable groups. J. Group Theory 14(2011), no. 1, 53–57. Google Scholar

[14] [14] Poimenidou, E. and Wolfe, H., Total characters and Chebyshev polynomials.Int. J. Math. Math. Sci.(2003), no. 38, 2447–2453. Google Scholar

[15] [15] Soto-Andrade, J., Geometrical Gelfand models, tensor quotients and Weil epresentations. Proc. Symp.Pure Math.47, Smer.Math.Soc, Providence, RI, 1987, pp. 306–316. Google Scholar

[16] [16] Tong-Viet, H. P., On groups with large character degree sums. Arch. Math. (Basel) 99(2012), no. 5, 401–405. Google Scholar | DOI

[17] [17] Zhang, J. and Li, X., Finite p-groups all of whose proper subgroups have cyclic Frattini subgroups.J. Group Theory 15(2012), no. 2, 245–259. Google Scholar

Cité par Sources :