What’s on the Group Axioms poster
9 entries in 2 groups.
A set G with one associative operation, an identity and inverses.
- The four axioms: Closure: ab lies in G for all a, b in G, Associativity: (ab)c = a(bc…
- What follows at once: The identity is unique, Each inverse is unique, (ab)⁻¹ = b⁻¹a⁻¹…
Commutativity is not an axiom. Matrix multiplication and function composition are the standard non-abelian examples.
Questions about the Group Axioms poster
- What’s on the Group Axioms poster?
- 9 entries in 2 groups. A set G with one associative operation, an identity and inverses. The four axioms: Closure: ab lies in G for all a, b in G, Associativity: (ab)c = a(bc…; What follows at once: The identity is unique, Each inverse is unique, (ab)⁻¹ = b⁻¹a⁻¹…. Commutativity is not an axiom. Matrix multiplication and function composition are the standard non-abelian examples.
- Who is the Group Axioms poster for?
- Group Axioms 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 Group Axioms poster?
- When checking a set with an operation really is a group. A wall chart earns its place by being glanceable from where the work is happening, so Group Axioms belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Group Axioms?
- Common Finite Groups, Cosets & Normal Subgroups and Cyclic Groups sit alongside Group Axioms 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 Group Axioms poster free to download and print?
- Yes. Group Axioms 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 Group Axioms poster print at?
- Group Axioms 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 Group Axioms loses nothing.Printing guide
Related posters
Charts that sit alongside Group Axioms on the same wall.
Browse every Mathematics poster, or start from the full catalogue.