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On commutative twisted group rings

Todor Zh. Mollov, Nako A. Nachev (2005)

Czechoslovak Mathematical Journal

Let G be an abelian group, R a commutative ring of prime characteristic p with identity and R t G a commutative twisted group ring of G over R . Suppose p is a fixed prime, G p and S ( R t G ) are the p -components of G and of the unit group U ( R t G ) of R t G , respectively. Let R * be the multiplicative group of R and let f α ( S ) be the α -th Ulm-Kaplansky invariant of S ( R t G ) where α is any ordinal. In the paper the invariants f n ( S ) , n { 0 } , are calculated, provided G p = 1 . Further, a commutative ring R with identity of prime characteristic p is said...

On complemented subgroups of finite groups

Long Miao (2006)

Czechoslovak Mathematical Journal

A subgroup H of a group G is said to be complemented in G if there exists a subgroup K of G such that G = H K and H K = 1 . In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about p -nilpotent groups.

On complete orbit spaces of SL(2) actions, II

Andrzej Białynicki-Birula, Joanna Święcicka (1992)

Colloquium Mathematicae

The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.

On computing quaternion quotient graphs for function fields

Gebhard Böckle, Ralf Butenuth (2012)

Journal de Théorie des Nombres de Bordeaux

Let Λ be a maximal 𝔽 q [ T ] -order in a division quaternion algebra over 𝔽 q ( T ) which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units Λ * on the Bruhat-Tits tree 𝒯 associated to PGL 2 ( 𝔽 q ( ( 1 / T ) ) ) . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group Λ * in terms of generators and relations. Moreover we determine an upper bound...

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