Characteristic Subgroups

Pole DC	Wartość	Język
dc.contributor.author	Nelson, Alexander M.	-
dc.date.accessioned	2022-12-30T10:52:01Z	-
dc.date.available	2022-12-30T10:52:01Z	-
dc.date.issued	2022	-
dc.identifier.citation	Formalized Mathematics, Volume 30, Issue 2, Pages 79-91	pl
dc.identifier.issn	1426-2630	-
dc.identifier.uri	http://hdl.handle.net/11320/14264	-
dc.description.abstract	We formalize in Mizar [1], [2] the notion of characteristic subgroups using the definition found in Dummit and Foote [3], as subgroups invariant under automorphisms from its parent group. Along the way, we formalize notions of Automorphism and results concerning centralizers. Much of what we formalize may be found sprinkled throughout the literature, in particular Gorenstein [4] and Isaacs [5]. We show all our favorite subgroups turn out to be characteristic: the center, the derived subgroup, the commutator subgroup generated by characteristic subgroups, and the intersection of all subgroups satisfying a generic group property.	pl
dc.language.iso	en	pl
dc.publisher	DeGruyter Open	pl
dc.rights	Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0)	pl
dc.rights.uri	https://creativecommons.org/licenses/by-sa/3.0/	pl
dc.subject	group theory	pl
dc.subject	inner automorphisms	pl
dc.subject	characteristic subgroups	pl
dc.title	Characteristic Subgroups	pl
dc.type	Article	pl
dc.rights.holder	© 2022 The Author(s)	pl
dc.rights.holder	CC BY-SA 3.0 license	pl
dc.identifier.doi	10.2478/forma-2022-0007	-
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.	pl
dc.description.references	Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.	pl
dc.description.references	David S. Dummit and Richard M. Foote. Abstract Algebra. Wiley and Sons, Third edition, 2004.	pl
dc.description.references	Daniel Gorenstein. Finite Groups. Chelsea Publishing Company, Second edition, 1980.	pl
dc.description.references	I. Martin Isaacs. Finite Group Theory, volume 92 of Graduate Studies in Mathematics. American Mathematical Society, 2008.	pl
dc.description.references	Marco Riccardi. The Jordan-Hölder theorem. Formalized Mathematics, 15(2):35–51, 2007. doi:10.2478/v10037-007-0005-8.	pl
dc.description.references	Wojciech A. Trybulec. Lattice of subgroups of a group. Frattini subgroup. Formalized Mathematics, 2(1):41–47, 1991.	pl
dc.description.references	Katarzyna Zawadzka. Solvable groups. Formalized Mathematics, 5(1):145–147, 1996.	pl
dc.identifier.eissn	1898-9934	-
dc.description.volume	30	pl
dc.description.issue	2	pl
dc.description.firstpage	79	pl
dc.description.lastpage	91	pl
dc.identifier.citation2	Formalized Mathematics	pl
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