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  2. List of problems in loop theory and quasigroup theory

    en.wikipedia.org/wiki/List_of_problems_in_loop...

    The first question is therefore open only in the infinite case. Call loop Q of Csörgõ type if it is nilpotent of class at least 3, and Inn(Q) is abelian. No loop of Csörgõ type of nilpotency class higher than 3 is known.

  3. Quasigroup - Wikipedia

    en.wikipedia.org/wiki/Quasigroup

    A quasigroup with an idempotent element is called a pique ("pointed idempotent quasigroup"); this is a weaker notion than a loop but common nonetheless because, for example, given an abelian group, (A, +), taking its subtraction operation as quasigroup multiplication yields a pique (A, −) with the group identity (zero) turned into a "pointed ...

  4. Small Latin squares and quasigroups - Wikipedia

    en.wikipedia.org/wiki/Small_Latin_squares_and...

    One can normalize a Cayley table of a quasigroup in the same manner as a reduced Latin square. Then the quasigroup associated to a reduced Latin square has a (two sided) identity element (namely, the first element among the row headers). A quasigroup with a two sided identity is called a loop. Some, but not all, loops are groups.

  5. Problems in loop theory and quasigroup theory - Wikipedia

    en.wikipedia.org/?title=Problems_in_loop_theory...

    Problems in loop theory and quasigroup theory. Add languages. ... Download QR code; Print/export Download as PDF; Printable version;

  6. Talk : List of problems in loop theory and quasigroup theory

    en.wikipedia.org/wiki/Talk:List_of_problems_in...

    Download QR code; Print/export Download as PDF; Printable version; This article is rated Start-class on ...

  7. Moufang loop - Wikipedia

    en.wikipedia.org/wiki/Moufang_loop

    Moufang loops are universal among inverse property loops; that is, a loop Q is a Moufang loop if and only if every loop isotope of Q has the inverse property. It follows that every loop isotope of a Moufang loop is a Moufang loop. One can use inverses to rewrite the left and right Moufang identities in a more useful form:

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  9. Loop group - Wikipedia

    en.wikipedia.org/wiki/Loop_group

    In its most general form a loop group is a group of continuous mappings from a manifold M to a topological group G.. More specifically, [1] let M = S 1, the circle in the complex plane, and let LG denote the space of continuous maps S 1 → G, i.e.

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