scholarly journals PROJECTIVE SPECIAL LINEAR GROUPS PSL4(q) ARE DETERMINED BY THE SET OF THEIR CHARACTER DEGREES

2012 ◽  
Vol 11 (06) ◽  
pp. 1250108 ◽  
Author(s):  
HUNG NGOC NGUYEN ◽  
HUNG P. TONG-VIET ◽  
THOMAS P. WAKEFIELD
Keyword(s):  
Finite Group ◽  
Character Degrees ◽  
Linear Groups ◽  
Complex Character ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
The Family ◽  
Group A ◽  
A Finite Group

Let G be a finite group and let cd (G) be the set of all irreducible complex character degrees of G. It was conjectured by Huppert in Illinois J. Math.44 (2000) that, for every non-abelian finite simple group H, if cd (G) = cd (H) then G ≅ H × A for some abelian group A. In this paper, we confirm the conjecture for the family of projective special linear groups PSL 4(q) with q ≥ 13.

RECOGNIZING BY ORDER AND DEGREE PATTERN OF SOME PROJECTIVE SPECIAL LINEAR GROUPS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250051 ◽  
Author(s):  
B. AKBARI ◽  
A. R. MOGHADDAMFAR
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Isomorphism Classes ◽  
Degree Pattern ◽  
A Finite Group

Let M be a finite group and D (M) be the degree pattern of M. Denote by h OD (M) the number of isomorphism classes of finite groups G with the same order and degree pattern as M. A finite group M is called k-fold OD-characterizable if h OD (M) = k. Usually, a 1-fold OD-characterizable group is simply called OD-characterizable. The purpose of this article is twofold. First, it provides some information on the structure of a group from its degree pattern. Second, it proves that the projective special linear groups L4(4), L4(8), L4(9), L4(11), L4(13), L4(16), L4(17) are OD-characterizable.

scholarly journals THE SUBGROUP COMMUTATIVITY DEGREE OF FINITE -GROUPS

2015 ◽  
Vol 93 (1) ◽  
pp. 37-41 ◽  
Author(s):  
MARIUS TĂRNĂUCEANU
Keyword(s):  
Finite Groups ◽  
Short Note ◽  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
The Family ◽  
Suzuki Groups

The subgroup commutativity degree of a group $G$ is the probability that two subgroups of $G$ commute, or equivalently that the product of two subgroups is again a subgroup. For the dihedral, quasi-dihedral and generalised quaternion groups (all of 2-power cardinality), the subgroup commutativity degree tends to 0 as the size of the group tends to infinity. This also holds for the family of projective special linear groups over fields of even characteristic and for the family of the simple Suzuki groups. In this short note, we show that the family of finite $P$-groups also has this property.

scholarly journals FACTORIZATION NUMBERS OF SOME FINITE GROUPS

2011 ◽  
Vol 54 (2) ◽  
pp. 345-354 ◽  
Author(s):  
F. SAEEDI ◽  
M. FARROKHI D. G.
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Groups ◽  
Dihedral Groups ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Cyclic Groups ◽  
General Linear Groups ◽  
A Finite Group ◽  
Projective General Linear Groups

AbstractFor a finite group G, let F2(G) be the number of factorizations G = AB of the group G, where A and B are subgroups of G. We compute F2(G) for certain classes of groups, including cyclic groups ℤn, elementary abelian p-groups ℤpn, dihedral groups D2n, generalised quaternion groups Q4n, quasi-dihedral 2-groups QD2n(n≥4), modular p-groups Mpn, projective general linear groups PGL(2, pn) and projective special linear groups PSL(2, pn).

scholarly journals Generating pairs of projective special linear groups that fail to lift

2020 ◽  
Vol 293 (7) ◽  
pp. 1251-1258
Author(s):  
Jan Boschheidgen ◽  
Benjamin Klopsch ◽  
Anitha Thillaisundaram
Keyword(s):  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups

A new characterization of Suzuki’s simple groups

2017 ◽  
Vol 16 (11) ◽  
pp. 1750216 ◽  
Author(s):  
Jinshan Zhang ◽  
Changguo Shao ◽  
Zhencai Shen
Keyword(s):  
Finite Group ◽  
Character Formula ◽  
Simple Groups ◽  
Complex Character ◽  
Group A ◽  
Vanishing Elements ◽  
A Finite Group

Let [Formula: see text] be a finite group. A vanishing element of [Formula: see text] is an element [Formula: see text] such that [Formula: see text] for some irreducible complex character [Formula: see text] of [Formula: see text]. Denote by Vo[Formula: see text] the set of the orders of vanishing elements of [Formula: see text]. In this paper, we prove that if [Formula: see text] is a finite group such that Vo[Formula: see text], [Formula: see text], then [Formula: see text].

scholarly journals A characterization of PGL (2,pn) by some irreducible complex character degrees

2016 ◽  
Vol 99 (113) ◽  
pp. 257-264 ◽  
Author(s):  
Somayeh Heydari ◽  
Neda Ahanjideh
Keyword(s):  
Finite Group ◽  
Prime Number ◽  
Cyclic Group ◽  
Group Algebra ◽  
Character Degrees ◽  
Complex Character ◽  
Complex Group ◽  
Complex Group Algebra ◽  
A Finite Group

For a finite group G, let cd(G) be the set of irreducible complex character degrees of G forgetting multiplicities and X1(G) be the set of all irreducible complex character degrees of G counting multiplicities. Suppose that p is a prime number. We prove that if G is a finite group such that |G| = |PGL(2,p) |, p ? cd(G) and max(cd(G)) = p+1, then G ? PGL(2,p), SL(2, p) or PSL(2,p) x A, where A is a cyclic group of order (2, p-1). Also, we show that if G is a finite group with X1(G) = X1(PGL(2,pn)), then G ? PGL(2, pn). In particular, this implies that PGL(2, pn) is uniquely determined by the structure of its complex group algebra.

scholarly journals HECKE ALGEBRAS FOR INNER FORMS OF -ADIC SPECIAL LINEAR GROUPS

2015 ◽  
Vol 16 (2) ◽  
pp. 351-419 ◽  
Author(s):  
Anne-Marie Aubert ◽  
Paul Baum ◽  
Roger Plymen ◽  
Maarten Solleveld
Keyword(s):  
Finite Group ◽  
Local Field ◽  
Hecke Algebras ◽  
Hecke Algebra ◽  
Linear Groups ◽  
Special Linear Groups ◽  
Affine Hecke Algebra ◽  
Morita Equivalent ◽  
Affine Hecke Algebras ◽  
A Finite Group

Let$F$be a non-Archimedean local field, and let$G^{\sharp }$be the group of$F$-rational points of an inner form of$\text{SL}_{n}$. We study Hecke algebras for all Bernstein components of$G^{\sharp }$, via restriction from an inner form$G$of$\text{GL}_{n}(F)$.For any packet of L-indistinguishable Bernstein components, we exhibit an explicit algebra whose module category is equivalent to the associated category of complex smooth$G^{\sharp }$-representations. This algebra comes from an idempotent in the full Hecke algebra of$G^{\sharp }$, and the idempotent is derived from a type for$G$. We show that the Hecke algebras for Bernstein components of$G^{\sharp }$are similar to affine Hecke algebras of type$A$, yet in many cases are not Morita equivalent to any crossed product of an affine Hecke algebra with a finite group.

Sign in / Sign up

Export Citation Format

Share Document