Multiplication groups of quasigroups and loops III.
Tomáš Kepka, A. Jančařík (1997)
Acta Universitatis Carolinae. Mathematica et Physica
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Displaying similar documents to “Multiplication groups of quasigroups and loops I.”
Multiplication groups of quasigroups and loops III.
Group theory based at any point.
Albar, M.A., Huq, S.A. (2001)
International Journal of Mathematics and Mathematical Sciences
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The Jordan-Hölder Theorem
Marco Riccardi (2007)
Formalized Mathematics
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The goal of this article is to formalize the Jordan-Hölder theorem in the context of group with operators as in the book [5]. Accordingly, the article introduces the structure of group with operators and reformulates some theorems on a group already present in the Mizar Mathematical Library. Next, the article formalizes the Zassenhaus butterfly lemma and the Schreier refinement theorem, and defines the composition series.
Connected transversals to subnormal subgroups
Tomáš Kepka, Jon D. Phillips (1997)
Commentationes Mathematicae Universitatis Carolinae
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Subnormal subgroups possessing connected transversals are briefly discussed.
Multiplication groups of quasigroups and loops IV.
A. Jančařík, Tomáš Kepka, Milan Vítek (2005)
Acta Universitatis Carolinae. Mathematica et Physica
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Solvable groups with many BFC-subgroups.
O. D. Artemovych (2000)
Publicacions Matemàtiques
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We characterize the solvable groups without infinite properly ascending chains of non-BFC subgroups and prove that a non-BFC group with a descending chain whose factors are finite or abelian is a Cernikov group or has an infinite properly descending chain of non-BFC subgroups.