2017
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Finite $2$groups of class $2$ with a specific automorphism group
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2
In this paper we determine all finite $2$groups of class $2$ in which every automorphism of order $2$ leaving the Frattini subgroup elementwise fixed is inner.
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S. Mohsen
Ghoraishi
Shahid Chamran university of Ahvaz
Shahid Chamran university of Ahvaz
Iran
m.ghoraishi@scu.ac.ir


Marzieh
Ahmadi
University of Isfahan
University of Isfahan
Iran
m_ahmadi@sci.ui.ac.ir
Finite $p$group of class $2$
noninner automorphism
Frattini subgroup
An extension and a generalization of Dedekind's theorem
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2
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroups. The factorizations is an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's theorem.
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Naoya
Yamaguchi
Kyushu University
Kyushu University
Japan
nyamaguchi@math.kyushuu.ac.jp
Dedekind's theorem
group determinant
group algebra