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A direct factor theorem for commutative group algebras

William Ullery (1992)

Commentationes Mathematicae Universitatis Carolinae

Suppose F is a field of characteristic p 0 and H is a p -primary abelian A -group. It is shown that H is a direct factor of the group of units of the group algebra F H .

A family of critically finite maps with symmetry.

Scott Crass (2005)

Publicacions Matemàtiques

The symmetric group Sn acts as a reflection group on CPn-2 (for n>=3).Associated with each of the (n2) transpositions in Sn is an involution on CPn-2 that pointwise fixes a hyperplane -the mirrors of the action. For each such action, there is a unique Sn-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations...

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