TY - JOUR
T1 - Group algebras whose group of units is powerful
AU - Bovdi, Victor
N1 - Funding Information:
The research was supported by OTKA No. K68383. ©c 2009 Australian Mathematical Publishing Association, Inc. 1446-7887/2009 $16.00
PY - 2009/12
Y1 - 2009/12
N2 - A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.
AB - A p-group is called powerful if every commutator is a product of pth powers when p is odd and a product of fourth powers when p=2. In the group algebra of a group G of p-power order over a finite field of characteristic p, the group of normalized units is always a p-group. We prove that it is never powerful except, of course, when G is abelian.
KW - Group of units
KW - Modular group algebra
KW - Powerful group
KW - Pro-p-group
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U2 - 10.1017/S1446788709000214
DO - 10.1017/S1446788709000214
M3 - Article
AN - SCOPUS:76449090641
SN - 1446-7887
VL - 87
SP - 325
EP - 328
JO - Journal of the Australian Mathematical Society
JF - Journal of the Australian Mathematical Society
IS - 3
ER -