The Symmetric GroupPermutations in cycle notation, with order and parity read straight off.MathematicsSₙ is the group of all rearrangements of n symbols.StructureSₙ contains every permutation of n symbols|Sₙ| = n!Non-abelian for every n ≥ 3Every element is a product of disjoint cyclesDisjoint cycles commute with each otherReading a permutationThe order of a single cycle is its lengthOrder overall is the lcm of cycle lengthsParity, even or odd, is well definedAₙ is the even permutations, of index 2Cayley: every group embeds in some SₙAₙ is simple for every n ≥ 5. That single fact is why the general quintichas no solution by radicals.The Symmetric Grouplearnposters.com
The Symmetric Group — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the The Symmetric Group poster

10 entries in 2 groups.

Sₙ is the group of all rearrangements of n symbols.

Aₙ is simple for every n ≥ 5. That single fact is why the general quintic has no solution by radicals.

Questions about the The Symmetric Group poster

What’s on the The Symmetric Group poster?
10 entries in 2 groups. Sₙ is the group of all rearrangements of n symbols. Structure: Sₙ contains every permutation of n symbols, |Sₙ| = n!, Non-abelian for eve…; Reading a permutation: The order of a single cycle is its length, Order overall is th…. Aₙ is simple for every n ≥ 5. That single fact is why the general quintic has no solution by radicals.
Who is the The Symmetric Group poster for?
The Symmetric Group belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning abstract algebra can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the The Symmetric Group poster?
Every finite group embeds in one of these, so they are the universal test case. A wall chart earns its place by being glanceable from where the work is happening, so The Symmetric Group belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with The Symmetric Group?
Common Finite Groups, Cosets & Normal Subgroups and Cyclic Groups sit alongside The Symmetric Group in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Common Finite GroupsCosets & Normal SubgroupsCyclic Groups
Is the The Symmetric Group poster free to download and print?
Yes. The Symmetric Group downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the The Symmetric Group poster print at?
The Symmetric Group is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of The Symmetric Group loses nothing.Printing guide

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