Isomorphism is a map between two groups, which is a bijection (one-to-one and onto) such that $f:G \rightarrow G'$. E.g., $f(x,y) = f(x)f(y)$ gives isomorphism.
In other words, an isomorphism $f:G \rightarrow G'$ is a homomorphism that is one-to-one and onto. $G$ is isomorphic to $G'$ is denoted by $G \simeq G'$.
Fact: Every two cyclic groups of order $n$ are isomorphic (Prove).
If the group is cyclic it means there is an element in it that generates the entire group.
-
- Active Topics
-
-
- by Eli 2 hours ago Re: What is in Your Mind? View the latest post Replies 687 Views 274105
- by Eli 1 day ago Iran Launches Retaliatory Attack Against Israel, and Israel Retaliates by Attacking Iranian Isfahan Millitary Base View the latest post Replies 28 Views 884
- by Eli 3 days ago All in One: YouTube, TED, X, Facebook and Instagram Reels, Videos, Images and Text Posts View the latest post Replies 319 Views 8967
- by Eli 5 days ago Python Packages for Scientific Computing View the latest post Replies 8 Views 3001
- by Eli 5 days ago Dunia Yetu: Building Tanzania's Digital Future Together View the latest post Replies 5 Views 1839
- by Eli 1 week ago Russia Invades Ukraine View the latest post Replies 646 Views 210460
- by Eli 1 week ago Programmatically Move Files from One Folder to Another View the latest post Replies 6 Views 1428
- by Eli 2 weeks ago Collection of Greatest Christian Hymns of all Times View the latest post Replies 33 Views 43741
- by Eli 2 weeks ago What is Retrieval-Augmented Generation (RAG)? View the latest post Replies 2 Views 358
- by Eli 2 weeks ago Chat With ChatGPT - An Interactive Conversational AI View the latest post Replies 22 Views 24361
-