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