Question

Eliminate contradiction in the definition of group of order $p^2$ with a normal subgroup of order $p$.

score 69 · Answer 1 · 2026-03-30 10:41:01

69

Views

Eliminate contradiction in the definition of group of order $p^2$ with a normal subgroup of order $p$.

Published on 30 Mar 2026 - 10:41

score 98 · Answer 2 · 2020-06-06 07:16:19

98

Views

Elementary proof that $\frac{\mathbb{K}^}{{\mathbb{K}^}^2}$ is infinite when $\mathbb{K}$ is a number field

Published on 06 Jun 2020 - 7:16

score 71 · Answer 3 · 2026-03-26 17:33:30

71

Views

Find the largest possible order of an element of $\frac{\Bbb{Z}_{12}\times\Bbb{Z}_3\times\Bbb{Z}_6}{\left<(8,2,4)\right>}.$

Published on 26 Mar 2026 - 17:33

score 337 · Answer 4 · 2020-06-07 20:37:05

337

Views

Proving $Ext_{\mathbb{Z}}^1(A,B)$ is a torsion-free abelian group, given that $A$ is divisible and $B$ is torsion-free

Published on 07 Jun 2020 - 20:37

score 101 · Answer 5 · 2026-03-30 10:41:05

101

Views

finding 3 groups that $G_1 \subsetneq G_2 \subsetneq G_3$ such that $G_1 \lhd G_2$ but $G_2 \not\lhd G_3$

Published on 30 Mar 2026 - 10:41

score 30 · Answer 6 · 2020-06-09 03:44:32

30

Views

For what kind of a $\bf{Z}$-Module there can always be found a $\bf{Z}$-Module homomorphism s.t. the diagram commutes

Published on 09 Jun 2020 - 3:44

score 803 · Answer 7 · 2026-03-26 17:33:15

803

Views

Let $N$ be a normal subgroup of $G$ and $H$ be a subgroup of $G$ such that $ H N =G$. Prove that $H$ is a system of representatives of $N$ in $G$.

Published on 26 Mar 2026 - 17:33

score 238 · Answer 8 · 2026-03-28 14:37:07

238

Views

Find all group homomorphisms $A_n \rightarrow \mathbb{C}^*$

Published on 28 Mar 2026 - 14:37

score 85 · Answer 9 · 2020-06-09 20:23:06

85

Views

Condition for the congruence class to form a subgroup of $\mathbb{Z}/n\mathbb{Z}$

Published on 09 Jun 2020 - 20:23

score 112 · Answer 10 · 2020-06-10 12:52:47

112

Views

Showing that if $\phi:\Bbb{Z}\oplus\Bbb{Z}\to\Bbb{Z}\oplus\Bbb{Z}$ is an epimorphism of abelian groups, then it is an isomorphism.

Published on 10 Jun 2020 - 12:52

score 27 · Answer 11 · 2020-06-10 19:37:04

27

Views

Finite Abelian group and subgroup

Published on 10 Jun 2020 - 19:37

score 203 · Answer 12 · 2020-06-11 11:38:31

203

Views

Group operation used in decomposition of Fundamental Theorem of Finite Abelian Groups

Published on 11 Jun 2020 - 11:38

score 3.8k · Answer 13 · 2026-03-28 07:57:12

3.8k

Views

Is a group of prime-power order always abelian?

Published on 28 Mar 2026 - 7:57

score 374 · Answer 14 · 2020-06-11 23:28:51

374

Views

Consider a set $G\subseteq \Bbb R$ and a binary operation * defined on $\Bbb R$ as $ab=a+b+ab$, such that $(G,)$ is an Abelian Group. Determine $G$.

Published on 11 Jun 2020 - 23:28

score 126 · Answer 15 · 2020-06-12 01:19:27

126

Views

Whats wrong with this 3d extension of the reals?

Published on 12 Jun 2020 - 1:19

List Question

Eliminate contradiction in the definition of group of order $p^2$ with a normal subgroup of order $p$.

Elementary proof that $\frac{\mathbb{K}^}{{\mathbb{K}^}^2}$ is infinite when $\mathbb{K}$ is a number field

Find the largest possible order of an element of $\frac{\Bbb{Z}_{12}\times\Bbb{Z}_3\times\Bbb{Z}_6}{\left<(8,2,4)\right>}.$

Proving $Ext_{\mathbb{Z}}^1(A,B)$ is a torsion-free abelian group, given that $A$ is divisible and $B$ is torsion-free

finding 3 groups that $G_1 \subsetneq G_2 \subsetneq G_3$ such that $G_1 \lhd G_2$ but $G_2 \not\lhd G_3$

For what kind of a $\bf{Z}$-Module there can always be found a $\bf{Z}$-Module homomorphism s.t. the diagram commutes

Let $N$ be a normal subgroup of $G$ and $H$ be a subgroup of $G$ such that $ H N =G$. Prove that $H$ is a system of representatives of $N$ in $G$.

Find all group homomorphisms $A_n \rightarrow \mathbb{C}^*$

Condition for the congruence class to form a subgroup of $\mathbb{Z}/n\mathbb{Z}$

Showing that if $\phi:\Bbb{Z}\oplus\Bbb{Z}\to\Bbb{Z}\oplus\Bbb{Z}$ is an epimorphism of abelian groups, then it is an isomorphism.

Finite Abelian group and subgroup

Group operation used in decomposition of Fundamental Theorem of Finite Abelian Groups

Is a group of prime-power order always abelian?

Consider a set $G\subseteq \Bbb R$ and a binary operation * defined on $\Bbb R$ as $ab=a+b+ab$, such that $(G,)$ is an Abelian Group. Determine $G$.

Whats wrong with this 3d extension of the reals?

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