brauer pairs
Recently Published Documents


TOTAL DOCUMENTS

9
(FIVE YEARS 1)

H-INDEX

1
(FIVE YEARS 0)

2021 ◽  
Vol 66 (4) ◽  
pp. 605-611
Author(s):  
Tiberiu Coconet ◽  

In this paper we give a generalization of a result of Puig and Zhou to the context of group graded algebras.We use this generalization for an alternative approach of the proof of a result involving group graded basic Morita equivalences.


2020 ◽  
Vol 23 (5) ◽  
pp. 925-930
Author(s):  
Morton E. Harris

AbstractLet k be an algebraically closed field of prime characteristic p. Let G be a finite group, let N be a normal subgroup of G, and let c be a G-stable block of kN so that {(kN)c} is a p-permutation G-algebra. As in Section 8.6 of [M. Linckelmann, The Block Theory of finite Group Algebras: Volume 2, London Math. Soc. Stud. Texts 92, Cambridge University, Cambridge, 2018], a {(G,N,c)}-Brauer pair {(R,f_{R})} consists of a p-subgroup R of G and a block {f_{R}} of {(kC_{N}(R))}. If Q is a defect group of c and {f_{Q}\in\operatorname{\textit{B}\ell}(kC_{N}(Q))}, then {(Q,f_{Q})} is a {(G,N,c)}-Brauer pair. The {(G,N,c)}-Brauer pairs form a (finite) poset. Set {H=N_{G}(Q,f_{Q})} so that {(Q,f_{Q})} is an {(H,C_{N}(Q),f_{Q})}-Brauer pair. We extend Lemma 8.6.4 of the above book to show that if {(U,f_{U})} is a maximal {(G,N,c)}-Brauer pair containing {(Q,f_{Q})}, then {(U,f_{U})} is a maximal {(H,C_{N}(c),f_{Q})}-Brauer pair containing {(Q,f_{Q})} and conversely. Our main result shows that the subcategories of {\mathcal{F}_{(U,f_{U})}(G,N,c)} and {\mathcal{F}_{(U,f_{U})}(H,C_{N}(Q),f_{Q})} of objects between and including {(Q,f_{Q})} and {(U,f_{U})} are isomorphic. We close with an application to the Clifford theory of blocks.


2008 ◽  
Vol 07 (05) ◽  
pp. 663-670 ◽  
Author(s):  
ADRIANA NENCIU

Two non-isomorphic finite groups form a Brauer pair if there exist a bijection for the conjugacy classes and a bijection for the irreducible characters that preserve all the character values and the power map. A group is called a VZ-group if all its nonlinear irreducible characters vanish off the center. In this paper we give necessary and sufficient conditions for two non-isomorphic VZ-groups to form a Brauer pair.


2006 ◽  
Vol 304 (1) ◽  
pp. 286-303 ◽  
Author(s):  
Bettina Eick ◽  
Jürgen Müller
Keyword(s):  

1999 ◽  
Vol 212 (2) ◽  
pp. 460-465
Author(s):  
Laurence Barker
Keyword(s):  

1990 ◽  
Vol 18 (10) ◽  
pp. 3437-3446
Author(s):  
Surinder K. Sehgal ◽  
Ron Solomon

Sign in / Sign up

Export Citation Format

Share Document