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33 Answers

newest activity votes
23
How to find pattern in $1,2,8,9,15,20,26,38…$ infinite sequence?
6
Prove or disprove that $\phi(a^n - 1)$ is divisible by n
5
Must $G$ be cyclic?
5
Is $e^x$ the only isomorphism between the groups $(\mathbb{R},+)$ and $(\mathbb{R}_{> 0},*)$?
5
Is there a number that's right in the middle of this interval $(0, 1)$?
4
If $R$ and $S$ are fields, either prove or disprove that $R\times S$ is a field
4
relaxing the assumptions of Euclid's lemma
4
Prove that the centralizer $C_K(H)$ has finite index in $K$
4
Interpolating between Krull-Schmidt and Jordan-Holder
4
how to find the root of permutation
4
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
3
Is an “open system” just a topological space?
3
Center and Fitting subgroups
3
Index of a group
2
Can the characteristic of some ring differ from number to number?
2
Finite groups with co-prime orders
2
Question related to commutator collection process and free groups
2
Inner automorphism of a subgroup
2
Claiming a finite set $S$, on which there is a binary operation $\bot$, to be a group by examining its multiplication table
2
Free group n contains subgroup of index 2
2
What's the process for finding a group with specific conditions for it's normal subgroups
1
$H$ must contain every Sylow $p$-subgroup of $G$
1
How do I show that $N\leqslant Z(G)$ without using Sylow theorems?
1
Let $a_i$ and $a_j$ disjoint cycles of $S_n$. Since $τ∈S_n$ is an one-to-one function, $τα_i τ^{-1}$ and $τα_jτ^{-1}$ must be also disjoint.
1
If $N \triangleleft G$ and $\mathrm{Aut}(N)=\mathrm{Inn}(N)$, show that $G=NC_G(N)$
1
Showing $(NM)/M \cong N/(N\cap M)$ for $N,M \triangleleft G$
1
A nontrivial p-group has nontrivial center
1
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
1
If $ H $ is a normal subgroup of $ G $, is $ G/H \times H \cong G $?
1
Dihedral group of degree 4 and sylow 3-subgroups.
1 2