Displaying similar documents to “A generalization of a theorem of A. D. Otto.”

On a group-theoretical generalization of the Gauss formula

Georgiana Fasolă, Marius Tărnăuceanu (2023)

Czechoslovak Mathematical Journal

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We discuss a group-theoretical generalization of the well-known Gauss formula involving the function that counts the number of automorphisms of a finite group. This gives several characterizations of finite cyclic groups.

Crossed product of cyclic groups

Ana-Loredana Agore, Dragoş Frățilă (2010)

Czechoslovak Mathematical Journal

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All crossed products of two cyclic groups are explicitly described using generators and relations. A necessary and sufficient condition for an extension of a group by a group to be a cyclic group is given.

Factoring an odd abelian group by lacunary cyclic subsets

Sándor Szabó (2010)

Discussiones Mathematicae - General Algebra and Applications

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It is a known result that if a finite abelian group of odd order is a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper gives an elementary proof that does not rely on characters.