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On certain algebras associated with finite groups

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Abstract

We construct new types of algebras which take into account the block structure of finite groups. We study the construction of such algebras. It is proved that the number of irreducible components of such an algebra is equal to the number of p blocks of the finite group whose defective groups contain a given p-element defined by the algebra. If the p-element is the unit, then the number of irreducible components is equal to the number of p-blocks of the finite group.

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Literature cited

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    K. Iizuka, “On Brauer's theorem on sections in the theory of blocks of group characters,” Math. Z.,75, 299–304 (1961).

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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 901–911, July–August, 1991.

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Gres', P.G. On certain algebras associated with finite groups. Ukr Math J 43, 841–849 (1991). https://doi.org/10.1007/BF01058680

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Keywords

  • Finite Group
  • Irreducible Component
  • Block Structure
  • Defective Group