TY - JOUR
T1 - Multiplicative Jordan decomposition in group rings of 3-groups
AU - Liu, Chia Hsin
AU - Passman, D. S.
N1 - Funding Information:
∗Research supported in part by NSC. †Research supported in part by NSA grant 144-LQ65.
PY - 2009
Y1 - 2009
N2 - In this paper, we essentially classify those finite 3-groups G having integral group rings with the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies MJD. Thus, we are only concerned with the nonabelian case. Here we show that ℤ[G] has the MJD property for the two nonabelian groups of order 33. Furthermore, we show that there are at most three other specific nonabelian groups, all of order 34, with ℤ[G] having the MJD property. Unfortunately, we are unable to decide which, if any, of these three satisfies the appropriate condition.
AB - In this paper, we essentially classify those finite 3-groups G having integral group rings with the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies MJD. Thus, we are only concerned with the nonabelian case. Here we show that ℤ[G] has the MJD property for the two nonabelian groups of order 33. Furthermore, we show that there are at most three other specific nonabelian groups, all of order 34, with ℤ[G] having the MJD property. Unfortunately, we are unable to decide which, if any, of these three satisfies the appropriate condition.
KW - 3-group
KW - Integral group ring
KW - Multiplicative Jordan decomposition
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U2 - 10.1142/S0219498809003461
DO - 10.1142/S0219498809003461
M3 - Article
AN - SCOPUS:70349456226
SN - 0219-4988
VL - 8
SP - 505
EP - 519
JO - Journal of Algebra and its Applications
JF - Journal of Algebra and its Applications
IS - 4
ER -