query: If two finite groups have the same number of elements of the same order, does this necessarily imply they are isomorphic?
positive_passages.docid: 29051
positive_passages.text: If I know the order of every element in a group, do I know the group?
negative_passages.docid: 83654
negative_passages.text: Order of an element in a finite cyclic group
negative_passages.docid: 45770
negative_passages.text: Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
negative_passages.docid: 46260
negative_passages.text: Prove that a group generated by two elements of order $2$, $x$ and $y$, is isomorphic to $D_{2n}$, where $n = |xy|.$
negative_passages.docid: 115649
negative_passages.text: Proving two sets $A, B$ are order isomorphic
negative_passages.docid: 114187
negative_passages.text: In a finite cyclic group, the generator has the order of the group
negative_passages.docid: 152481
negative_passages.text: If order of group is $p^2$, where $p$ is prime, how can you deduce $G$ is isomorphic to $C_{p^2}$ or $C_p \times C_p$?
negative_passages.docid: 2731
negative_passages.text: Groups of even order have an element whose order is 2.
negative_passages.docid: 74455
negative_passages.text: Can a single sentence be used to distinguish between isomorphic classes of finite structures?
negative_passages.docid: 1577
negative_passages.text: Order of nontrivial elements is 2 implies Abelian group
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: 67374
negative_passages.text: Is it true that $\mathbb{R}$ and $\mathbb{R}^2$ are isomorphic as abelian groups?
negative_passages.docid: 116594
negative_passages.text: Finite fields are isomorphic
negative_passages.docid: 107511
negative_passages.text: If $G$ and $H$ are nonisomorphic group with same order then can we say that $Aut(G)$ is not isomorphic to $Aut(H)$?
negative_passages.docid: 6189
negative_passages.text: Examples of infinite groups such that all their respective elements are of finite order.
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: 152603
negative_passages.text: Group isomorphic to its automorphism group