TY - JOUR
T1 - Symmetric subgroups in modular group algebras
AU - Konovalov, Alexander
AU - Krivokhata, A. G.
N1 - This preprint is translated from the original journal publication in Russian: A. Konovalov and A. Tsapok, Symmetric subgroups of the normalised unit group of the modular group algebra of a finite p-group, Nauk. Visn. Uzhgorod. Univ., Ser. Mat., 9 (2004), 20–24.
PY - 2008/1/5
Y1 - 2008/1/5
N2 - Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=, where S* is a set of symmetric units of V(KG).
AB - Let V(KG) be a normalised unit group of the modular group algebra of a finite p-group G over the field K of p elements. We introduce a notion of symmetric subgroups in V(KG) as subgroups invariant under the action of the classical involution of the group algebra KG. We study properties of symmetric subgroups and construct a counterexample to the conjecture by V.Bovdi, which states that V(KG)=, where S* is a set of symmetric units of V(KG).
KW - math.RA
KW - math.GR
KW - 16S34
KW - 20C05
KW - Rings and Algebras
KW - Group Theory
UR - http://arxiv.org/abs/0801.0809
M3 - Article
VL - 9
JO - Nauk. Visn. Uzhgorod. Univ., Ser. Mat.,
JF - Nauk. Visn. Uzhgorod. Univ., Ser. Mat.,
ER -