I came across this sign when reading some papers. I looked up Wikipedia. It says "The symbol "$\\cong$" is often used to indicate isomorphic algebraic structures or congruent geometric …

In mathematical notation, what are the usage differences between the various approximately-equal signs "≈", "≃", and "≅"? The Unicode standard lists all of them inside the Mathematical …

Sep 28, 2024 · Claim: $\operatorname {Hom}_ {G} (V,W) \cong \operatorname {Hom}_ {G} (\mathbf {1},V^ {*} \otimes W)$ I'm looking for hints as to how to approach the proof of this claim.

Nov 13, 2015 · A symbol I have in my math homework looks like a ~ above a =. (That is, $\\cong$.) What does this mean? I'm studying Congruency at the moment if that helps.

Prove that $\mathbb Z_ {m}\times\mathbb Z_ {n} \cong \mathbb Z_ {mn}$ implies $\gcd (m,n)=1$. This is the converse of the Chinese remainder theorem in abstract algebra.

Jan 1, 2025 · I went through several pages on the web, each of which asserts that $\operatorname {Aut} A_n \cong \operatorname {Aut} S_n \; (n\geq 4)$ or an equivalent …

In convex quadrilateral ABCD, A B C D, ∠A ≅ ∠C, ∠ A ≅ ∠ C, AB = CD = 180, A B = C D = 180, and AD ≠ BC. A D ≠ B C. The perimeter of ABCD A B C D is ...

The homomorphism involved here is defined as a ∈ G ↦ σa ∈ Inn(G) a ∈ G ↦ σ a ∈ Inn (G) where σa σ a is a bijection from G G to G G with σa(x) = axa−1 σ a (x) = a x a 1. The details can be …

Jan 5, 2022 · I think you might have the right idea because: hom$_R (R,M)\cong M$, think about why? You can think about hom$_R (R/I,M)$, as a subset of hom$_R (R,M)$, maybe the first …

Mar 9, 2021 · As the title insinuates, in my readings I can across this isomorphism H ⊗C ≅EndC(H) H ⊗ C ≅ End C (H) and i cannot see why this is the case. Can someone help me …