query: Proof that the $(\mathcal P (\mathbb N),\triangle)$ is an abelian group?
positive_passages.docid: 26572
positive_passages.text: Does the Symmetric difference operator define a group on the powerset of a set?
negative_passages.docid: 23533
negative_passages.text: All subgroups normal $\implies$ abelian group
negative_passages.docid: 115204
negative_passages.text: Show that SO(n) is a normal subgroup of O(n)
negative_passages.docid: 7015
negative_passages.text: Prove that if $(ab)^i = a^ib^i \forall a,b\in G$ for three consecutive integers $i$ then G is abelian
negative_passages.docid: 51359
negative_passages.text: Prove that every subgroup of an abelian group is a normal subgroup.
negative_passages.docid: 26624
negative_passages.text: Prove that is group is abelian
negative_passages.docid: 108425
negative_passages.text: Problem on abelian group
negative_passages.docid: 38153
negative_passages.text: Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 17510
negative_passages.text: Proving a set is an abelian group.
negative_passages.docid: 106091
negative_passages.text: Showing $\mathcal{P}(X)$ is isomorphic to $2^X$
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: 126893
negative_passages.text: A group of order 2p (p prime) and other conditions - prove abelian.
negative_passages.docid: 74964
negative_passages.text: Showing Galois Group is Abelian
negative_passages.docid: 13742
negative_passages.text: Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
negative_passages.docid: 15387
negative_passages.text: Order of $GL(n, \mathbb Z_p)$
negative_passages.docid: 135039
negative_passages.text: ${\rm Aut}(G)$ is cyclic $\implies G$ is abelian