query: Prove a set with this associative operation is a group
positive_passages.docid: 14097
positive_passages.text: A semigroup $X$ is a group iff for every $g\in X$, $\exists! x\in X$ such that $gxg = g$
negative_passages.docid: 24181
negative_passages.text: Showing that $G$ is a group under an alternative operation.
negative_passages.docid: 115649
negative_passages.text: Proving two sets $A, B$ are order isomorphic
negative_passages.docid: 133498
negative_passages.text: Show that Function Compositions Are Associative
negative_passages.docid: 1707
negative_passages.text: How does one prove that addition on $\mathbb{R}$ is associative?
negative_passages.docid: 5226
negative_passages.text: Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
negative_passages.docid: 64527
negative_passages.text: Show that an operation of elements in a finite group contains each element exactly once
negative_passages.docid: 37951
negative_passages.text: proof detail concerning bijection between a set and its power set
negative_passages.docid: 43759
negative_passages.text: Prove that the set $\mathrm{Aut}(G)$ of all automorphisms of the group $G$ with the operation of taking the composition is a group
negative_passages.docid: 51896
negative_passages.text: Prove that: set $\{1, 2, 3, ..., n - 1\}$ is group under multiplication modulo $n$?
negative_passages.docid: 142631
negative_passages.text: Show that A has the same cardinality as $A\setminus\{x,y,z\}$
negative_passages.docid: 103695
negative_passages.text: Prove Inverses not need be Unique if Associativity fails
negative_passages.docid: 70164
negative_passages.text: Proof exercise that the cardinal number of a set in $\mathbb R^2$ is $\frak c$
negative_passages.docid: 18817
negative_passages.text: Does commutativity imply Associativity?
negative_passages.docid: 44405
negative_passages.text: Prove XOR is commutative and associative?
negative_passages.docid: 114522
negative_passages.text: Prove that identity is unique in a group
negative_passages.docid: 77286
negative_passages.text: Proving set theory question