Recognition of PSL(2,p) ×PSL(2,p) by its complex group algebra

2017 ◽  
Vol 16 (02) ◽  
pp. 1750036 ◽  
Author(s):  
Behrooz Khosravi ◽  
Zahra Momen ◽  
Behnam Khosravi ◽  
Bahman Khosravi
Keyword(s):  
Prime Number ◽  
Group Algebra ◽  
Character Degrees ◽  
Simple Groups ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Quasisimple Group ◽  
Natural Groups ◽  
Groups Of Lie Type

In [H. P. Tong-Viet, Simple classical groups of Lie type are determined by their character degrees, J. Algebra 357 (2012) 61–68] the following question arose: Question. Which groups can be uniquely determined by the structure of their complex group algebras? It is proved that every quasisimple group except covers of the alternating groups is uniquely determined up to isomorphism by the structure of [Formula: see text], the complex group algebra of [Formula: see text]. One of the next natural groups to be considered are the characteristically simple groups. In this paper, as the first step in this investigation we prove that if [Formula: see text] is an odd prime number, then [Formula: see text] is uniquely determined by the structure of its complex group algebra.

Complex group algebras of the direct product of non-isomorphic Suzuki groups

2019 ◽  
Vol 19 (02) ◽  
pp. 2050036
Author(s):  
Morteza Baniasad Azad ◽  
Behrooz Khosravi
Keyword(s):  
Direct Product ◽  
Group Algebra ◽  
Irreducible Character ◽  
Prime Numbers ◽  
Product Formula ◽  
Character Degrees ◽  
Group Algebras ◽  
Complex Group ◽  
Complex Group Algebra ◽  
Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

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.

WARFIELD INVARIANTS IN COMMUTATIVE GROUP ALGEBRAS

2008 ◽  
Vol 07 (03) ◽  
pp. 337-346 ◽  
Author(s):  
PETER V. DANCHEV
Keyword(s):  
Abelian Group ◽  
Prime Number ◽  
Group Algebra ◽  
Ordinal Number ◽  
Commutative Group ◽  
Group Algebras

Let F be a field and G an Abelian group. For every prime number q and every ordinal number α we compute only in terms of F and G the Warfield q-invariants Wα, q(VF[G]) of the group VF[G] of all normed units in the group algebra F[G] under some minimal restrictions on F and G. This expands own recent results from (Extracta Mathematicae, 2005) and (Collectanea Mathematicae, 2008).

scholarly journals Moore-Penrose inversion in complex contracted inverse semigroup algebras

1999 ◽  
Vol 66 (3) ◽  
pp. 297-302
Author(s):  
W. D. Munn
Keyword(s):  
Inverse Semigroup ◽  
Group Algebra ◽  
Semigroup Algebra ◽  
Semigroup Algebras ◽  
Locally Finite ◽  
Complex Group ◽  
Complex Group Algebra

AbstractIt is shown that every element of the complex contracted semigroup algebra of an inverse semigroup S = S0 has a Moore-Penrose inverse, with respect to the natural involution, if and only if S is locally finite. In particular, every element of a complex group algebra has such an inverse if and only if the group is locally finite.

scholarly journals On the Modular Version of Ito’s Theorem on Character Degrees for Groups of Odd Order

1987 ◽  
Vol 105 ◽  
pp. 109-119 ◽  
Author(s):  
Olaf Manz
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Prime Number ◽  
Character Degrees ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Classical Representation ◽  
Odd Order ◽  
Complex Characters

One of the most useful theorems in classical representation theory is a result due to N. Ito, which can be stated using the classification of the finite simple groups in the following way.THEOREM (N. Ito, G. Michler). Let Irr (G) be the set of all irreducible complex characters of the finite group G and q be a prime number. Then if and only if G has a normal, abelian Sylow-q-subgroup.

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