query: A monoid with left identity and right inverses need not be a group
positive_passages.docid: 152191
positive_passages.text: Why is a monoid with right identity and left inverse not necessarily a group?
negative_passages.docid: 117479
negative_passages.text: Mutual set of representatives for left and right cosets: what about infinite groups?
negative_passages.docid: 138273
negative_passages.text: Terminology for a monoid with a total ordering on the elements?
negative_passages.docid: 126771
negative_passages.text: Group element not taken to its inverse by any automorphism
negative_passages.docid: 87534
negative_passages.text: Finitely generated group which is not finitely presented
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 3203
negative_passages.text: Quotient group $\mathbb Z^n/\ \text{im}(A)$
negative_passages.docid: 118898
negative_passages.text: Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
negative_passages.docid: 114522
negative_passages.text: Prove that identity is unique in a group
negative_passages.docid: 85379
negative_passages.text: Semigroup analogue to the classification of finite simple groups?
negative_passages.docid: 6755
negative_passages.text: A finite, cancellative semigroup is a group
negative_passages.docid: 120557
negative_passages.text: Group of invertible elements of a ring has never order $5$
negative_passages.docid: 109072
negative_passages.text: Find the left cosets of subroups of $S_3$
negative_passages.docid: 46875
negative_passages.text: The identity morphism in $\mathbf{Set}$ is the identity function
negative_passages.docid: 112407
negative_passages.text: Set of left cosets is a group
negative_passages.docid: 125613
negative_passages.text: Free idempotent semigroup with 3 generators
negative_passages.docid: 74452
negative_passages.text: On a uniqueness proof for solutions of $\ a + x = b\,$ in a group