Math

### Questions (42)

 17 Groups of order $180$, $540$, $1080$ are not simple. 8 Abelian subgroup contained in a normal subgroup; a trick about elements of order $3$ 7 $p$-groups in which the centralizers are normal 5 When every minimal subgroup is contained in the center 5 Any simple group of order $60$ is isomorphic to $A_5$

### Reputation (963)

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 1 How to determine $\prod_{g\in G}g$ in all generality 1 For homomorphism $\phi: G\to H$, if $G_{1}\leq G$ and $|G_{1}|=n$, then $|\phi(G_{1})|$ divides $n$. 1 Let $|a|=m$ and $|b|=n$ and $gcd(m,n)=1$. Show that $\left \langle a \right \rangle \cap \left \langle b \right \rangle = \left \{ e \right \}$. 0 Subnormality of normalizers 0 A question on characteristically simple groups

### Tags (29)

 3 group-theory × 44 1 group-homomorphism 1 finite-groups × 15 0 abstract-algebra × 31 1 proof-verification × 6 0 simple-groups × 6 1 proof-explanation × 4 0 normal-subgroups × 4 1 cyclic-groups × 2 0 abelian-groups × 4