What’s on the Common Finite Groups poster
A 7-row table: Group · Order · Notes.
The examples every proof is tested against.
- ℤₙ — n — Cyclic, so abelian
- Sₙ — n! — All permutations of n
- Aₙ — n!/2 — The even permutations
- Dₙ — 2n — Symmetries of an n-gon
- Q₈ — 8 — Quaternions, non-abelian
- Klein four group — 4 — Abelian but not cyclic
- GL(n, F) — Varies — Invertible n×n matrices
Every group of order p is cyclic, and every group of order p² is abelian. The smallest non-abelian group is S₃, of order 6.
Questions about the Common Finite Groups poster
- What’s on the Common Finite Groups poster?
- A 7-row table: Group · Order · Notes. The examples every proof is tested against. ℤₙ — n — Cyclic, so abelian; Sₙ — n! — All permutations of n; Aₙ — n!/2 — The even permutations; Dₙ — 2n — Symmetries of an n-gon; Q₈ — 8 — Quaternions, non-abelian; Klein four group — 4 — Abelian but not cyclic; GL(n, F) — Varies — Invertible n×n matrices. Every group of order p is cyclic, and every group of order p² is abelian. The smallest non-abelian group is S₃, of order 6.
- Who is the Common Finite Groups poster for?
- Common Finite Groups 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 Common Finite Groups poster?
- Before believing a claim about all groups, check it against these. A wall chart earns its place by being glanceable from where the work is happening, so Common Finite Groups belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Common Finite Groups?
- Cosets & Normal Subgroups, Cyclic Groups and First Isomorphism Theorem sit alongside Common Finite Groups in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Cosets & Normal SubgroupsCyclic GroupsFirst Isomorphism Theorem
- Is the Common Finite Groups poster free to download and print?
- Yes. Common Finite Groups 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 Common Finite Groups poster print at?
- Common Finite Groups 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 Common Finite Groups loses nothing.Printing guide
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