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Tour:Getting started (beginners)

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Part four
{{quotation|[[Guided tour for beginners:Introduction One|Get started]]}}We are about to get started on the guided tour for beginners. To get the most from this guided tour, stay faithful to it, i.e. read the articles in the order suggested. You will have various opportunities for detours: some other articles to read so as to get a better understanding of what you're touring, and some just for entertainment. Please try to open these ''detours'' in different windows/tabs so that you do not lose track of where you are in the main tour.__NOTOC__
This tour is not Guided tours are intended to be a complete introduction to group theoryan online equivalent of textbooks, or with a replacement for textbook or course materialslot more flexibility. RatherYou read through a collection of pages, it is intended as a supplement. To get the most adapted from this tour, keep open your main course book or lecture notes and make sure you can ''map'' what's there on the wikito be used as learning resources, and are then presented with what you're learning in the course or from the textbooka set of exercises and review tools.
So far, only one guided tour has been in preparation -- the guided tour for beginners. This was initially developed in 2008, but was not completed as the focus shifted to first improving the overall quality of the site. The portion of the tour is structured as followscreated so far covers basic definitions of groups, subgroups, cosets, and Lagrange's theorem, along with a number of exercises.
==Part one=={{quotation|'''There is a lot more material on the website than what is covered in the guided tour.''' If you are interested in reading up material on the website that may be relevant for beginners, try using the search bar, and also look within these categories: [[:Category:Basic definitions in group theory]], [[:Category:Basic facts in group theory]], [[:Category:Elementary non-basic facts in group theory]].<br>Based on user experience, the following topics, which will ''eventually'' be part of the guided tour, but are not yet included in it, are very popular among people who are doing/have just completed an introductory course in group theory: [[symmetric group:S3]] (also, its [[element structure of symmetric group:S3|elements]], [[subgroup structure of symmetric group:S3|subgroups]], and [[linear representation theory of symmetric group:S3|representations]]), [[symmetric group:S4]] (also, its [[element structure of symmetric group:S4|elements]], [[subgroup structure of symmetric group:S4|subgroups]], and [[linear representation theory of symmetric group:S4|representations]]), and [[dihedral group:D8]] (also, its [[element structure of dihedral group:D8|elements]], [[subgroup structure of dihedral group:D8|subgroups]], and [[linear representation theory of dihedral group:D8|representations]]).}}
{{quotation|Get started with [[Guided tour for beginnersTour:Introduction one(beginners)|Get started]]}}This part provides We are about to get started on the guided tour for beginners. To get the most from this guided tour, stay faithful to it, i.e. read the articles in the order suggested. You will have various opportunities for detours: some very basicother articles to read so as to get a better understanding of what you're touring, introductory definitionsand some just for entertainment. We Please try to open these ''detours'' in different windows/tabs so that you do not focus here on lose track of where you are in the example-oriented motivation for these definitionsmain tour. The definitions provided are:
* [[Guided This tour for beginners:Group|is not intended to be a complete introduction to group]]* [[Guided tour theory, or a replacement for beginners:Abelian group|Abelian group]]* [[Guided tour for beginners:Subgroup|Subgroup]]* [[Guided textbook or course materials. Rather, it is intended as a supplement. To get the most from this tour for beginners:Trivial group|Trivial group]]* [[Guided tour for beginners:Verifying , keep open your main course book or lecture notes and make sure you can ''map'' what's there on the group axioms|Verifying wiki, with what you're learning in the group axioms]]* [[Guided tour for beginners:Understanding course or from the definition of a group|Understanding the definition of a group]]Prerequisites for this part:textbook.
* An understanding of set-theoretic notation* A basic understanding Before starting, you should read the [[Tour:General instructions (beginners)|general instructions]]. You may also find it useful to read the [[Tour:Pedagogical notes (beginners)|pedagogical notes]] that explain the structure of functions between sets, unary and binary operations, and relationsthe tour in more detail.
The goal of this part tour is to:structured as follows.
* Provide a basic understanding of the definitions of group, subgroup, trivial group, and Abelian group* Provide the skill of determining whether a set with a binary operation, forms a group==Part one==
{{quotation|Get started with [[Tour:Introduction one (beginners)]]}}
{{#lst:Tour:Introduction one (beginners)|pagelist}}
{{#lst:Tour:Introduction one (beginners)|prerequisite}}
{{#lst:Tour:Introduction one (beginners)|goal}}
==Part two==
{{quotation|Get started with [[Guided tour for beginnersTour:Introduction two(beginners)]]}}
This part focuses on providing an understanding of how to do simple manipulations involving groups. We begin by generalizing some of the ideas involving groups, and discussing proofs involving some of the basic manipulations.
Prerequisites{{#lst: Part one Tour:Introduction two (or equivalentbeginnersThe goal of this part is to give comfort in simple manipulations involving groups. Articles covered in this part are: * [[Guided tour for beginners:Some variations of group|Some variations of group]]pagelist}}* [[Guided tour for beginners{{#lst:Equality of left and right neutral element|Equality of left and right neutral element]]* [[Guided tour for beginnersTour:Equality of left and right inverses|Equality of left and right inverses]]* [[Guided tour for Introduction two (beginners:Equivalence of definitions of group)|Equivalence of definitions of group]]prerequisite}}* [[Guided tour for beginners{{#lst:Invertible implies cancellative|Invertible implies cancellative]]* [[Guided tour for beginnersTour:Associative binary operation|Associative binary operation]]* [[Guided tour for Introduction two (beginners:Finite group)|Finite group]]* [[Guided tour for beginners:Subsemigroup of finite group is subgroup|Subsemigroup of finite group is subgroup]]* [[Guided tour for beginners:Sufficiency of subgroup criterion|Sufficiency of subgroup criterion]]* [[Guided tour for beginners:Manipulating equations in groups|Manipulating equations in groups]] Continue to [[Guided tour for beginners:Group|the definition of a group]]goal}}
==Part three==
{{quotation|Get started with [[Guided tour for beginnersTour:Introduction three(beginners)]]}} Prerequisites{{#lst: Part two or equivalent This part focuses a bit more on subgroups; the notion of intersection and union of subgroups and whether a union of subgroups is a subgroup. * [[Guided tour for beginnersTour:Intersection of subgroups is subgroup|Intersection of subgroups is subgroup]]* [[Guided tour for Introduction three (beginners:Union of two subgroups is not a subgroup)|Union of two subgroups is not a subgroup]]pagelist}}* [[Guided tour for beginners{{#lst:Left coset of a subgroup|Left coset of a subgroup]]* [[Guided tour for beginnersTour:Left cosets are in bijection via left multiplication|Left cosets are in bijection via left multiplication]]* [[Guided tour for Introduction three (beginners:Right coset of a subgroup)|Right coset of a subgroup]]prerequisite}}* [[Guided tour for beginners{{#lst:Left and right coset spaces are naturally isomorphic|Left and right coset spaces are naturally isomorphic]]* [[Guided tour for beginnersTour:Lagrange's theorem|Lagrange's theorem]]* [[Guided tour for Introduction three (beginners:Generating set of a group)|Generating set of a group]]* [[Guided tour for beginners:Subgroup generated by a subset|Subgroup generated by a subset]]* [[Guided tour for beginners:Join of subgroups|Join of subgroups]]* [[Guided tour for beginners:Some examples of groups and subgroups|Some examples of groups and subgroups]]goal}}
==Part four==
''Not yet prepared'' * [[Guided tour for beginners:Homomorphism of groups|Homomorphism of groups]]* [[Guided tour for beginners:Isomorphism of groups|Isomorphism of groups]]* [[Guided tour for beginners:Isomorphic groups|Isomorphic groups]]* [[Guided tour for beginners:Endomorphism of a group|Endomorphism of a group]]* [[Guided tour for beginners:Automorphism of a group|Automorphism of a group]]* [[Guided tour for beginners:Automorphism group|Automorphism group]]* [[Guided tour for beginners:Inner automorphism|Inner automorphism]]* [[Guided tour for beginners:Kernel|Kernel]]* [[Guided tour for beginners:Normal subgroup|Normal subgroup]]* [[Guided tour for beginners:Quotient group|Quotient group]]* [[Guided tour for beginners:First isomorphism theorem|First isomorphism theorem]]* [[Guided tour for beginners:Second isomorphism theorem|Second isomorphism theorem]]* [[Guided tour for beginners:Third isomorphism theorem{{quotation|Third isomorphism theorem]] ==Part five==''Not yet prepared''* Get started with [[Guided tour for beginnersTour:Characteristic subgroup|Characteristic subgroup]]* [[Guided tour for Introduction four (beginners:Characteristic implies normal|Characteristic implies normal)]]}}* [[Guided tour for beginners{{#lst:External direct product|External direct product]]* [[Guided tour for beginnersTour:Internal direct product|Internal direct product]]* [[Guided tour for Introduction four (beginners:Group property)|Group property]]pagelist}}* [[Guided tour for beginners{{#lst:Subgroup property|Subgroup property]]* [[Guided tour for beginnersTour:Subgroup-defining function|Subgroup-defining function]]* [[Guided tour for Introduction four (beginners:Center)|Center]]prerequisite}}* [[Guided tour for beginners{{#lst:Characteristic of normal implies normal|Characteristic of normal implies normal]]* [[Guided tour for beginnersTour:Commutator subgroup|Commutator subgroup]]* [[Guided tour for Introduction four (beginners:Normality is strongly intersection-closed)|Normality is strongly intersection-closed]]* [[Guided tour for beginners:Normality is strongly join-closed|Normality is strongly join-closed]]* [[Guided tour for beginners:Invariance property|Invariance property]]goal}}
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