## The Sylow Theorems

The goal of this article is to formalize the Sylow theorems closely following the book [4]. Accordingly, the article introduces the group operating on a set, the stabilizer, the orbits, the *p*-groups and the Sylow subgroups.

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## The Sylow Theorems

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*Formalized Mathematics*, 2011, Volume 19, Number 1*Formalized Mathematics*, 2008, Volume 16, Number 2

In This Section# Formalized Mathematics

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Editor-in-Chief: Matuszewski, Roman

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Source Normalized Impact per Paper (SNIP) 2016: 0.315

Marco Riccardi

The goal of this article is to formalize the Sylow theorems closely following the book [4]. Accordingly, the article introduces the group operating on a set, the stabilizer, the orbits, the *p*-groups and the Sylow subgroups.

[1] Grzegorz Bancerek. Cardinal numbers.

*Formalized Mathematics*, 1(2):377-382, 1990.Google Scholar[2] Grzegorz Bancerek. The ordinal numbers.

*Formalized Mathematics*, 1(1):91-96, 1990.Google Scholar[3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences.

*Formalized Mathematics*, 1(1):107-114, 1990.Google Scholar[4] Nicolas Bourbaki.

*Elements of Mathematics. Algebra I. Chapters 1-3.*Springer-Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, 1989.Google Scholar[5] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets.

*Formalized Mathematics*, 1(3):529-536, 1990.Google Scholar[6] Czesław Byliński. Functions and their basic properties.

*Formalized Mathematics*, 1(1):55-65, 1990.Google Scholar[7] Czesław Byliński. Functions from a set to a set.

*Formalized Mathematics*, 1(1):153-164, 1990.Google Scholar[8] Czesław Byliński. Partial functions.

*Formalized Mathematics*, 1(2):357-367, 1990.Google Scholar[9] Czesław Byliński. Some basic properties of sets.

*Formalized Mathematics*, 1(1):47-53, 1990.Google Scholar[10] Czesław Byliński. The sum and product of finite sequences of real numbers.

*Formalized Mathematics*, 1(4):661-668, 1990.Google Scholar[11] Agata Darmochwał. Finite sets.

*Formalized Mathematics*, 1(1):165-167, 1990.Google Scholar[12] Artur Korniłowicz. The definition and basic properties of topological groups.

*Formalized Mathematics*, 7(2):217-225, 1998.Google Scholar[13] Rafał Kwiatek. Factorial and Newton coefficients.

*Formalized Mathematics*, 1(5):887-890, 1990.Google Scholar[14] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes.

*Formalized Mathematics*, 1(5):829-832, 1990.Google Scholar[15] Karol Pak. Cardinal numbers and finite sets.

*Formalized Mathematics*, 13(3):399-406, 2005.Google Scholar[16] Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction.

*Formalized Mathematics*, 1(3):441-444, 1990.Google Scholar[17] Dariusz Surowik. Cyclic groups and some of their properties - part I.

*Formalized Mathematics*, 2(5):623-627, 1991.Google Scholar[18] Andrzej Trybulec. Subsets of complex numbers.

*To appear in Formalized Mathematics.*Google Scholar[19] Andrzej Trybulec. Domains and their Cartesian products.

*Formalized Mathematics*, 1(1):115-122, 1990.Google Scholar[20] Andrzej Trybulec. Tarski Grothendieck set theory.

*Formalized Mathematics*, 1(1):9-11, 1990.Google Scholar[21] Michał J. Trybulec. Integers.

*Formalized Mathematics*, 1(3):501-505, 1990.Google Scholar[22] Wojciech A. Trybulec. Classes of conjugation. Normal subgroups.

*Formalized Mathematics*, 1(5):955-962, 1990.Google Scholar[23] Wojciech A. Trybulec. Groups.

*Formalized Mathematics*, 1(5):821-827, 1990.Google Scholar[24] Wojciech A. Trybulec. Subgroup and cosets of subgroups.

*Formalized Mathematics*, 1(5):855-864, 1990.Google Scholar[25] Wojciech A. Trybulec and Michał J. Trybulec. Homomorphisms and isomorphisms of groups. Quotient group.

*Formalized Mathematics*, 2(4):573-578, 1991.Google Scholar[26] Zinaida Trybulec. Properties of subsets.

*Formalized Mathematics*, 1(1):67-71, 1990.Google Scholar[27] Edmund Woronowicz. Relations and their basic properties.

*Formalized Mathematics*, 1(1):73-83, 1990.Google Scholar[28] Edmund Woronowicz. Relations defined on sets.

*Formalized Mathematics*, 1(1):181-186, 1990.Google Scholar

**Published Online**: 2008-06-09

**Published in Print**: 2007-01-01

**Citation Information: **Formalized Mathematics, ISSN (Online) 1898-9934, ISSN (Print) 1426-2630, DOI: https://doi.org/10.2478/v10037-007-0018-3.

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[1]

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[2]

Marco Riccardi

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