List questions from abstract-algebra

Published on 17 Apr 2026 - 14:10

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When $2$-cycles (transpositions) are not disjoint, they don't necessarily commute?

Published on 13 Apr 2026 - 17:40

40

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Prove that $( \mathbb Z ^x _n , \odot)$ is a group

Published on 15 Apr 2026 - 11:41

1k

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Prove that the general linear group, GL(V) is a group

Published on 14 Apr 2026 - 21:55

216

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Find the splitting field of a polynomial over $Z_{p}$

Published on 11 Apr 2026 - 21:41

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Prove that there are $2n$ distinct symmetries of the regular $n$-gon.

Published on 15 Apr 2026 - 14:15

91

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Special linear group, efficient square roots calculation

Published on 11 Apr 2026 - 17:08

305

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When does there exist a non-cyclic group of size $pq$?

Published on 14 Apr 2026 - 10:14

176

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Prove that a dihedral set is a group

Published on 14 Apr 2026 - 9:25

132

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Using elementary ring theory to show that $\langle xy^3, x^2y^2, x^3y\rangle$ cannot be generated by 2 elements over $\mathbb{C}[x,y]$

Published on 15 Apr 2026 - 17:16

176

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Is the $2\times 2$ matrix a group?

Published on 09 Apr 2026 - 9:58

64

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Are these statements about reducible polynomials correct?

Published on 11 Apr 2026 - 17:41

81

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How can I show $(x^2+1, y^2+1)$ is not maximal in $\mathbb R[x,y]$? Is there a geometric interpretation for this?

Published on 15 Apr 2026 - 4:56

79

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Concerning the proof pf the Eisenstein's Criterion

Published on 13 Apr 2026 - 12:23

327

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Is $P/Z(P)$ cyclic when $Z(P)$ is not trivial?

Published on 18 Apr 2026 - 15:07

List Question

Sum of $1/(1 - x)$ over roots of unity

When $2$-cycles (transpositions) are not disjoint, they don't necessarily commute?

Prove that $( \mathbb Z ^x _n , \odot)$ is a group

Prove that the general linear group, GL(V) is a group

Find the splitting field of a polynomial over $Z_{p}$

Prove that there are $2n$ distinct symmetries of the regular $n$-gon.

Special linear group, efficient square roots calculation

When does there exist a non-cyclic group of size $pq$?

Prove that a dihedral set is a group

Using elementary ring theory to show that $\langle xy^3, x^2y^2, x^3y\rangle$ cannot be generated by 2 elements over $\mathbb{C}[x,y]$

Is the $2\times 2$ matrix a group?

Are these statements about reducible polynomials correct?

How can I show $(x^2+1, y^2+1)$ is not maximal in $\mathbb R[x,y]$? Is there a geometric interpretation for this?

Concerning the proof pf the Eisenstein's Criterion

Is $P/Z(P)$ cyclic when $Z(P)$ is not trivial?

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