query: Does group inverse commute with multiplication for all groups?
positive_passages.docid: 25439
positive_passages.text: f(a) = inverse of a is an isomorphism iff a group G is Abelian
negative_passages.docid: 25430
negative_passages.text: When is matrix multiplication commutative?
negative_passages.docid: 156247
negative_passages.text: Question about permutations and cycles (Groups and Symmetries)
negative_passages.docid: 43326
negative_passages.text: Can every group be represented by a group of matrices?
negative_passages.docid: 100549
negative_passages.text: If $e^A$ and $e^B$ commute, do $A$ and $B$ commute?
negative_passages.docid: 17997
negative_passages.text: Right identity and Right inverse implies a group
negative_passages.docid: 123860
negative_passages.text: When are two direct products of groups isomorphic?
negative_passages.docid: 37414
negative_passages.text: Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
negative_passages.docid: 120495
negative_passages.text: Does this correctly interpret the "$\cong$" between groups as "$=$" between sets?
negative_passages.docid: 31421
negative_passages.text: Transpose inverse automorphism is not inner
negative_passages.docid: 157582
negative_passages.text: Inverse of $ab$ and its order in a group with relations $a^2=e=b^6$ and $ab=b^4a$
negative_passages.docid: 64372
negative_passages.text: Do the isomorphism's of groups form an equivalence relation on the class of all groups?
negative_passages.docid: 21958
negative_passages.text: Splitting of conjugacy class in alternating group
negative_passages.docid: 39425
negative_passages.text: Surprising but simple group theory result on conjugacy classes
negative_passages.docid: 73382
negative_passages.text: A concrete example of involution in group theory
negative_passages.docid: 30676
negative_passages.text: $G'$ and the product of all the elements in an odd order group
negative_passages.docid: 35124
negative_passages.text: Can every non-simple group $G$ be written as a semidirect product?