Displaying similar documents to “Intermittent-assertion method as a structural induction”

Holomorph of generalized Bol loops II

Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá, Bolaji Ajibola Popoola (2015)

Discussiones Mathematicae - General Algebra and Applications

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The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some...

Relatives of K-loops: Theory and examples

Hubert Kiechle (2000)

Commentationes Mathematicae Universitatis Carolinae

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A or is a Bol loop with the automorphic inverse property. An overview of the most important theorems on K-loops and some of their relatives, especially Kikkawa loops, is given. First, left power alternative loops are discussed, then Kikkawa loops are considered. In particular, their nuclei are determined. Then the attention is paid to general K-loops and some special classes of K-loops such as 2-divisible ones. To construct examples, the method of is introduced. This has been used...