4 Let $a$ be an element of a group $G$ and $|a| = 7.$ Show $a$ is the cube of some element of $G$. 2 Prescription of mapping f: N x N → N which is not injection and surjection 1 Show that $N(a)= \{ x \in G | x\circ a = a \circ x \}$ is a sub-group when $(G,\circ)$ is a group. 1 If $(U^c,+,*)$ is maximal ideal ($U$ group formed by unit elements) then $A/U^c$ is a fields? 1 The set of natural number is semi group?

### Reputation (418)

 +50 Prove that every ideal of $R=\mathbb{Z}[x]$ can be generated by at most two elements of $R$ +10 Show that $N(a)= \{ x \in G | x\circ a = a \circ x \}$ is a sub-group when $(G,\circ)$ is a group. +2 Let $n = 4k$ or $n = 4k+1$ for non-negative $k$. Prove that there exist a self-complementary graph $G = (V, E)$, where $|V| =n$ +2 Is $( P(X), *)$ a group if: 1. $A*B = A \cup B$ and 2. $A*B = A \cap B$?

### Questions (12)

 5 Prove that every ideal of $R=\mathbb{Z}[x]$ can be generated by at most two elements of $R$ 5 Relation between kernel of groups and Semigroups 4 Graph Homomorphism 1 Why we have $| \mathcal{F}(X\times Y, Z)|=| \mathcal{F}(Y, \mathcal{F}(X, Z))|$ [closed] 0 Semilattice of idempotent

### Tags (25)

 6 group-theory × 8 1 ring-theory × 3 2 discrete-mathematics 1 field-theory 1 abstract-algebra × 8 1 proof-verification 1 semigroups × 5 1 general-topology 1 elementary-set-theory × 3 1 definition

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