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Groups
  • Member for 11 years, 11 months
  • Last seen more than 8 years ago
33 votes
Accepted

Construct a non-abelian group of order 75

25 votes

Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$

14 votes

Give an example of a nonabelian group in which a product of elements of finite order can have infinite order.

13 votes
Accepted

A Group Having a Cyclic Sylow 2-Subgroup Has a Normal Subgroup.

13 votes
Accepted

Difference between a group normalizer and centralizer

12 votes
Accepted

What is Amalgamation

9 votes

${\rm Aut}(G)$ is cyclic $\implies G$ is abelian

7 votes
Accepted

How many roots have modulus less than $1$?

7 votes
Accepted

Proof using binomial Theorem

7 votes

Generators of the symmetric group

7 votes

Intuition of coset of a subgroup

6 votes

Grasping the concept of equivalence classes more concretely

6 votes
Accepted

Finding Sylow 2-subgroups of the dihedral group $D_n$

6 votes
Accepted

Group of Order 105 Having Normal Sylow 5/7 Subgroups

5 votes

Proof that finite group contains an element of prime order

4 votes

Commutator Subgroup in a $p$-group

4 votes
Accepted

Subgroups of index $p$ in additive group $\mathbb{Z}^2$?

4 votes

Diamond Isomorphism Theorem clarification.

4 votes

o(a)=m ,o (b) =n , ab=ba then o(ab)=lcm(m,n). What happens when b is the inverse of a?

4 votes

Group of order $48$ must have a normal subgroup of order $8$ or $16$

4 votes
Accepted

commutator subgroup of upper triangular matrix

4 votes
Accepted

Characteristic subgroups and automorphisms

4 votes

The intersection of an infinite number of prime ideals in a ring of integers

4 votes
Accepted

Determine the sign of the permutation $f \circ g \circ f \circ g \circ f \circ g \circ f$

4 votes
Accepted

If $|G|=24$ or $48,36,56,72,80,90$ or $96$ prove that $G$ is an abelian or simple group .

4 votes
Accepted

If $(G, \circ)$ is a finite group with identity $e$, prove that there exists a positive integer $m$ such that $a^m=e$ holds for all $a\in G$.

4 votes

problem book on Group theory after doing Fraleigh.

4 votes
Accepted

number of non trivial group homomorphisms

3 votes
Accepted

Group homomorphism from $SL_2 (\mathbb Z / 5 \mathbb Z)$ to $S_5$

3 votes
Accepted

quotient group G/N order and isomorphic group