3 research outputs found
Finite semisimple group algebra of a normally monomial group
In this paper, the complete algebraic structure of finite semisimple group
algebra of a normally monomial group is described. The main result is
illustrated by computing the explicit Wedderburn decomposition of finite
semisimple group algebras of various normally monomial groups. The automorphism
groups of these group algebras are also determined.Comment: 20 page
A note on an inverse problem in algebra
In this paper, we discuss the inverse problem of determining a semisimple
group algebra from the knowledge of rings of the type sum_{t=1}^s M_{n_t}(Ft),
where j is an arbitrary integer and F_t is finite field for each t, and show
that it is ill-posed. After then, we define the concept of completeness of the
rings of the type sum_{t=1}^s M_{n_t}(Ft) to pose a well-posed inverse problem
and propose a conjecture in this direction
Semisimple finite group algebra of a generalized strongly monomial group
The complete algebraic structure of semisimple finite group algebra of a
generalized strongly monomial group is provided. This work extends the work of
Broche and del R{\'{\i}}o on strongly monomial groups. The theory is
complimented by an algorithm and is illustrated with an example