6 research outputs found
Unitary Units of The Group Algebra
The structure of the unitary unit group of the group algebra {\F}_{2^k}
Q_{8} is described as a Hamiltonian group.Comment: 4 page
Units in
In this paper, we present the structure of the group of *-unitary units in
the group algebra , where is a finite field of characteristic , is the dihedral group of order , and * is the canonical
involution of the group algebra . We also provide the structure of the
maximal -subgroup of the unit group and compute a
basis of its center.Comment: 15 page
Isomorphism problem of Unitary Subgroups of Group Algebras
Let V_* be the normalized unitary subgroup of the modular group algebra FG of
a finite p-group G over a finite field F with the classical involution *. We
investigate the isomorphism problem for the group V_*, that asks when the group
V_* is determined by its group algebra FG. We confirm it for classes of finite
abelian p-groups, 2-groups of maximal class and non-abelian 2-groups of order
at most 16.Comment: 10 page
Unitary Subgroups of commutative group algebras of characteristic two
Let be the group algebra of a finite -group over a finite field
of characteristic two and an involution which arises from
. The -unitary subgroup of , denoted by
, is defined to be the set of all normalized units
satisfying the property . In this paper we establish
the order of for all involutions which
arise from , where is a finite cyclic -group and show that all
-unitary subgroups of are not isomorphic
On the Unitary Subgroups of group algebras
Let be the group algebra of a finite -group over a finite field
of characteristic and the classical involution of . The
-unitary subgroup of , denoted by , is defined to be the set of
all normalized units satisfying the property . In this paper we
give a recursive method how to compute the order of the -unitary subgroup
for many non-commutative group algebras. We also prove a variant of the modular
isomorphism question of group algebras, where is a finite field of
characteristic two, that is determines the basic group for all
non-abelian -groups of order at most
Unit Groups of Some Group Rings
Let be the gruop ring of the group over ring and
be its unit group. Finding the structure of the unit group of
a finite group ring is an old topic in ring theory. In, G. Tang et al: Unit
Groups of Group Algebras of Some Small Groups. Czech. Math. J. 64 (2014),
149--157, the structure of the unit group of the group ring of the non abelian
group with order over any finite field of characteristic 3 was
established. In this paper, we are going to generalize their result to any non
abelian group , where .Comment: Submitted to Czechoslovak Mathematical Journa