Over a field of characteristic p the group algebra of a finite group has a non-trivial radical if
and only if the order of the group is divisible by the prime p. It would be of interest to …

Over a field of prime characteristic p the group algebra of a finite group has a non-trivial
radical if and only if the order of the group is divisible by the prime p. In two earlier papers [7 …

Let J (KG) be the Jacobson radical of the group algebra KG of a finite p-solvable group G
over a field K of characteristic p> 0, and let t (G) be the least positive integer t such that J …

It is well known that when the characteristic p (≠ 0) of a field divides the order of a finite
group, the group algebra possesses a non-trivial radical and that, if p does not divide the …

Let G be a finite group of order pam where p is prime and (p, m)= 1. Let Q be an
algebraically closed field of characteristic p. We consider the group algebra A (G, Q) of G …

A basic result in the study of group algebras and characters states that the group algebra 3I
(gp) of a finite group g" over the field g of characteristic p Φ 0 has a nonzero radical 9ΐ if and …

Let K be an arbitrary field with characteristic p> 0, G a finite group of order pag′ with (p,
g′)= 1, P a p-Sylow subgroup of G and G′ the commutator subgroup of G. For a ring R …

Introduction. It is known that when the characteristic p (+ 0) of a field divides the order of a
group, the group algebra over that field is not semi-simple and so possesses a radical. An …

In this note we consider the radical of the centre of the group algebra of a finite group over a
field of non-zero characteristic, and characterise those soluble groups for which this radical …

1. RESULTS The Jacobson radicals of group algebras have received the attention of many
authors over the years and several problems have remained unsolved. For example (see [#] …