Displaying similar documents to “The Semidirect Products of Finite Cyclic Groups That Are I-E Groups.”

Schreier type theorems for bicrossed products

Ana Agore, Gigel Militaru (2012)

Open Mathematics

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We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ...

Units of F5kD10

Gildea, Joe (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33. The Structure of the Unit Group of the Group Algebra of the group D10 over any field of characteristic 5 is established in terms of split extensions of 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.