The multiplicative Jordan decomposition in the integral group ring Z[Q8×Cp]
نویسندگان
چکیده
منابع مشابه
Multiplicative Jordan Decomposition in Group Rings of 3-groups, Ii
In this paper, we complete the classification of those finite 3groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. In the nonabelian case, we show that Z[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.
متن کاملMultiplicative Jordan Decomposition in Group Rings of 2, 3-groups
In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that Z[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, ...
متن کاملMultiplicative Jordan Decomposition in Group Rings of 3-groups
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 o...
متن کاملMultiplicative Jordan Decomposition in Group Rings with a Wedderburn Component of Degree 3
IfG is a finite group whose integral group ring Z[G] has the multiplicative Jordan decomposition property, then it is known that all Wedderburn components of the rational group ring Q[G] have degree at most 3. While degree 3 components can occur, we prove here that if they do, then certain central units in Z[G] cannot exist. With this, we are able to greatly simplify the argument that character...
متن کاملAppendix - Multiplicative Jordan Decomposition in Group Rings of 2, 3-groups
In this appendix, we offer a reasonably self-contained proof that the " generalized quater-nion group " Q 12 of order 12 has the MJD property.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2019
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2019.06.015