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Central ideals and Jacobson radicals of blocks of group algebras
Yoshihiro Otokita
We study the relationship between the central ideals and the Jacobson radicals of blocks of group algebras.In particular, we characterize the blocks with the property that the squa…
Loewy lengths of centers of blocks and exponents of defect groups
Yoshihiro Otokita
In this paper we study the Loewy structure of the center of a block of a finite group with respect to an algebraically closed field of prime characteristic. We first state a n…
Notes on Loewy series of centers of -blocks
Yoshihiro Otokita
The present paper describes some results on the Loewy series of the center of a modular group algebra in order to solve a problem on the number of irreducible ordinary characters.…
Loewy lengths of centers of blocks II
Burkhard Külshammer, Yoshihiro Otokita, Benjamin Sambale
Let ZB be the center of a p-block B of a finite group with defect group D. We show that the Loewy length LL(ZB) of ZB is bounded by provided D is not cyclic. If…
On centers of blocks with non-cyclic defect groups
Yoshihiro Otokita
In this short note we study the center ZB of a block B of a finite group over an algebraically closed field of prime characteristic through its Loewy length llZB. A result of Okuya…
Some studies on Loewy lengths of centers of p-blocks
Yoshihiro Otokita
In this paper, we investigate some relations between the Loewy lengths of the centers of blocks of group algebras and its defect groups. In particular, we give a new upper bound of…
On diagonal entries of Cartan matrices of p-blocks
Yoshihiro Otokita
In this short note, we show some inequalities on Cartan matrices, centers and socles of blocks of group algebras. Our main theorems are generalizations of the facts on dimension of…