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Automorphism groups of right-angled buildings: simplicity and local splittings

Pierre-Emmanuel Caprace (2014)

Fundamenta Mathematicae

We show that the group of type-preserving automorphisms of any irreducible semiregular thick right-angled building is abstractly simple. When the building is locally finite, this gives a large family of compactly generated abstractly simple locally compact groups. Specialising to appropriate cases, we obtain examples of such simple groups that are locally indecomposable, but have locally normal subgroups decomposing non-trivially as direct products, all of whose factors are locally normal.

Basic subgroups in abelian group rings

Peter Vassilev Danchev (2002)

Czechoslovak Mathematical Journal

Suppose R is a commutative ring with identity of prime characteristic p and G is an arbitrary abelian p -group. In the present paper, a basic subgroup and a lower basic subgroup of the p -component U p ( R G ) and of the factor-group U p ( R G ) / G of the unit group U ( R G ) in the modular group algebra R G are established, in the case when R is weakly perfect. Moreover, a lower basic subgroup and a basic subgroup of the normed p -component S ( R G ) and of the quotient group S ( R G ) / G p are given when R is perfect and G is arbitrary whose G / G p is p -divisible....

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