query: $H\otimes l^{2}(\Gamma)\cong\bigoplus\limits_{g\in \Gamma}H$
positive_passages.docid: 17191
positive_passages.text: How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$
negative_passages.docid: 102284
negative_passages.text: $GL(n,\mathbb R)/SL(n,\mathbb R)$ is isomophic to $\mathbb R^\times$
negative_passages.docid: 36142
negative_passages.text: What is $\mathbb Z \oplus \mathbb Z / \langle (2,2) \rangle$ isomorphic to?
negative_passages.docid: 151621
negative_passages.text: $G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$
negative_passages.docid: 76100
negative_passages.text: Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
negative_passages.docid: 4648
negative_passages.text: Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
negative_passages.docid: 129732
negative_passages.text: What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?
negative_passages.docid: 65141
negative_passages.text: Simple proof Euler–Mascheroni $\gamma$ constant
negative_passages.docid: 133238
negative_passages.text: Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
negative_passages.docid: 141683
negative_passages.text: $ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
negative_passages.docid: 91085
negative_passages.text: how to find $|GL_2(F_p)|$
negative_passages.docid: 78592
negative_passages.text: Tensor product of Hadamard operators
negative_passages.docid: 67199
negative_passages.text: Isomorphism $H_n(D^n, S^{n - 1};A)$ and $A$
negative_passages.docid: 89659
negative_passages.text: $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
negative_passages.docid: 120010
negative_passages.text: Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
negative_passages.docid: 73458
negative_passages.text: Double cover of $GL(n,\mathbb{C})$.
negative_passages.docid: 128256
negative_passages.text: How to prove $H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ to the lattice $\Lambda$ ,$\gamma \mapsto \int_\gamma dz$ is well defined?