Groups with the same complex group algebras as some extensions of psl(2, pn)
-
Somayeh Heydari
and
Neda Ahanjideh
Abstract
For a natural number n and the prime p, let L be an almost simple group with the socle PSL(2,pn) such that p does not divide [L: PSL(2,pn)]. In this paper, we prove that L is uniquely determined by the first column of its character table. In particular, this implies that L is uniquely determined by the structure of its complex group algebra.
Research partially supported by the center of Excellence for Mathematics, University of Shahrekord, Iran.
References
[1] Berkovich, Y.—Zhmud, E.: Characters of Finite Groups, Part 1. Transl. Math. Monogr., Vol. 172, Amer. Math. Soc., 1997.10.1090/mmono/172Search in Google Scholar
[2] Heydari, S.—Ahanjideh, N.: A characterization of PGL(2, pn) by some irreducible complex character degrees, Publications de l’Institut Mathematique, 99 (2016), 257–264.10.2298/PIM150111017HSearch in Google Scholar
[3] Heydari, S.—Ahanjideh, N.: Characterization of some simple K4-groups by some irreducible complex character degrees, Int. J. Group theory, 5 (2016), 61–74.Search in Google Scholar
[4] Huppert, B.: Character Theory of Finite Groups, de Gruyter, Berlin/New York, 1998.10.1515/9783110809237Search in Google Scholar
[5] Huppert, B.: Some simple groups which are determined by the set of their character degrees (I), Illinois J. Math. 44 (2000), 828–842.10.1215/ijm/1255984694Search in Google Scholar
[6] Isaacs, I. M.: Character Theory of Finite Groups, Academic Press, New York, 1976.Search in Google Scholar
[7] Isaacs, I. M.— Moreto, A.—Navaro, G.— Huu Tiep, P.: Groups with just one character degree divisible by a given prime, Trans. Amer. Math. Soc. 361 (2009), 6521–6547.10.1090/S0002-9947-09-04718-7Search in Google Scholar
[8] Tong-Viet, H. P.: Simple classical groups of Lie type are determined by their character degrees, J. Algebra 357 (2012), 61–68.10.1016/j.jalgebra.2012.02.011Search in Google Scholar
[9] Xu, H.— Yan, Y. —Chen, G.: A new characterization of Mathieu-groups by the order and one irreducible character degree, J. Ineq. Appl. 10.1186/1029-242X-2013-209.Search in Google Scholar
[10] White, D. L: Character degrees of extensions of PSL(2, q), J. Group Theory 16 (2013), 1–33.10.1515/jgt-2012-0026Search in Google Scholar
© 2017 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
-
Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
- A note on groups with finite conjugacy classes of subnormal subgroups
- Groups with the same complex group algebras as some extensions of psl(2, pn)
- Klee-Phelps convex groupoids
- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
- A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
Articles in the same Issue
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
-
Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
- A note on groups with finite conjugacy classes of subnormal subgroups
- Groups with the same complex group algebras as some extensions of psl(2, pn)
- Klee-Phelps convex groupoids
- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
- A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
