# luke

less info
reputation
416
bio website location age member for 1 year, 11 months seen Dec 13 at 4:49 profile views 61

 12 What needs to be true of $f$ for $f_{xy}=f_{yx}$? 7 cyclic group and its generators 6 Finding elements of order $8$ in $\mathbb{Z}_{8000000}$. 5 Finite Groups: $a \in G \implies a \in H$ 4 The Derivative of $\cos(x-2)$

# 878 Reputation

 +5 Strategy for determining the number of homomorphisms between two Groups +5 Let $\alpha$ be a $2$-cycle and $\beta$ be a $t$-cycle in $S_n$. Prove that $\alpha\beta\alpha$ is a $t$-cycle +5 Prove that $G \cong\mathrm{Inn}(G)$ if and only if $Z(G)$ is trivial +15 Another Uniform Convergence problem

# 8 Questions

 7 Prove that $G \cong\mathrm{Inn}(G)$ if and only if $Z(G)$ is trivial 4 Strategy for determining the number of homomorphisms between two Groups 4 In $S_7$, $x^2=(1234)$ has no solutions but $x^3=(1234)$ has at least two 3 Prove that $x \in Z(G) \to G \ncong \text{Inn}(G)$. [duplicate] 2 Can we take an $i$th root?

# 24 Tags

 34 group-theory × 19 4 symmetric-groups × 2 29 abstract-algebra × 16 4 abelian-groups 21 calculus × 5 3 morphism × 2 14 finite-groups × 8 2 permutation-groups × 2 7 derivatives × 3 2 functions

# 1 Account

 Mathematics 878 rep 416