Displaying similar documents to “Structure of unitary groups over finite group rings and its application”

Inertias and ranks of some Hermitian matrix functions with applications

Xiang Zhang, Qing-Wen Wang, Xin Liu (2012)

Open Mathematics

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Let S be a given set consisting of some Hermitian matrices with the same size. We say that a matrix A ∈ S is maximal if A − W is positive semidefinite for every matrix W ∈ S. In this paper, we consider the maximal and minimal inertias and ranks of the Hermitian matrix function f(X,Y) = P − QXQ* − TYT*, where * means the conjugate and transpose of a matrix, P = P*, Q, T are known matrices and for X and Y Hermitian solutions to the consistent matrix equations AX =B and YC = D respectively....

On the structure of the augmentation quotient group for some nonabelian 2-groups

Jizhu Nan, Huifang Zhao (2012)

Czechoslovak Mathematical Journal

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Let G be a finite nonabelian group, ℤ G its associated integral group ring, and ▵ ( G ) its augmentation ideal. For the semidihedral group and another nonabelian 2-group the problem of their augmentation ideals and quotient groups Q n ( G ) = ▵ n ( G ) / ▵ n + 1 ( G ) is deal with. An explicit basis for the augmentation ideal is obtained, so that the structure of its quotient groups can be determined.