### Questions (150)

 26 What is the flaw in my thinking for the graph of this function? 12 Herstein or Herstein? 11 Constant rank theorem: intuition? 10 What's the definition of a “local property”? 7 The order of $ab$ when $a,b$ commute

### Reputation (3,955)

 +10 The order of $ab$ when $a,b$ commute +10 Constant rank theorem: intuition? +10 Difference between cellular and simplicial homology +10 Proof that half of the subgroup is even

 3 In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime. 2 Prove that $\{\beta \in S_5 \mid \beta(1)=1, \beta(3)=3\}$ is a subgroup of $S_5$ 2 Let G be a group with exactly two nontrivial proper subgroups. Show that G is cyclic. What are the possible orders of G? 1 Proving a homomorphism is surjective. 1 Showing that elements in a finite group is odd and even

### Tags (60)

 11 group-theory × 66 2 permutations × 3 4 abstract-algebra × 8 1 elementary-number-theory × 8 3 cyclic-groups × 2 1 number-theory 3 p-groups 0 differential-geometry × 49 2 finite-groups × 5 0 proof-verification × 30

### Bookmarks (38)

 52 Geometric understanding of differential forms. 20 Different definitions of a “one-form” 17 Is it true that the order of $ab$ is always equal to the order of $ba$? 16 An element of a group has the same order as its inverse 16 Prove that if the identity is written as the product of $r$ transpositions, then $r$ is an even number