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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 the derived length of units in group algebra

Dishari Chaudhuri, Anupam Saikia (2017)

Czechoslovak Mathematical Journal

Let G be a finite group G , K a field of characteristic p 17 and let U be the group of units in K G . We show that if the derived length of U does not exceed 4 , then G must be abelian.

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