TY - JOUR
ID - 5452
TI - Sylow like theorems for $V(\mathbb{Z}G)$
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Kimmerle, Wolfgang
AD - University of Stuttgart
Y1 - 2015
PY - 2015
VL - 4
IS - 4
SP - 49
EP - 59
KW - Group rings
KW - integral group ring
KW - Subgroup isomorphism problem
DO - 10.22108/ijgt.2015.5452
N2 - The main part of this article is a survey on torsion subgroups of the unit group of an integral group ring. It contains the major parts of my talk given at the conference "Groups, Group Rings and Related Topics" at UAEU in Al Ain October 2013. In the second part special emphasis is layed on $p$ - subgroups and on the open question whether there is a Sylow like theorem in the normalized unit group of an integral group ring. For specific classes of finite groups we prove that $p$ - subgroups of the normalized unit group of its integral group rings $V(\mathbb{Z}G)$ are isomorphic to subgroups of $G .$ In particular for $p = 2$ this is shown when $G$ has abelian Sylow $2$ - subgroups. This extends results known for soluble groups to classes of groups which are not contained in the class of soluble groups.
UR - https://ijgt.ui.ac.ir/article_5452.html
L1 - https://ijgt.ui.ac.ir/article_5452_1c109992064605dc78186ce51e795fb6.pdf
ER -