Commutative Group Algebras and Prüfer Groups

Suppose G is a multiplicatively written abelian p-group, where p is a prime, and F is a field of arbitrary characteristic. The main results in this paper are that none of the Sylow p-group of all normalized units S(FG) in the group ring FG and its quotient group S(FG)/G cannot be Prüfer groups. This contrasts a classical conjecture for which S(FG)/G is a direct factor of a direct sum of generalized Prüfer groups whenever F is a perfect field of characteristic p.

並列關鍵字

Prüfer groups ； cyclic groups ； direct sums of cyclic groups ； units ； Ulm-Kaplansky invariants ； direct factors

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Commutative Group Algebras and Prüfer Groups

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