List questions from cyclic-groups

Published on 17 Apr 2026 - 0:42

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On a special type of finite abelian groups of prime power order

Published on 05 May 2026 - 4:16

37

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Transpositions and permutations algebraic proeprties

Published on 13 Apr 2026 - 5:06

119

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Group theory, subgroup of index 2

Published on 29 Apr 2026 - 12:54

77

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Number of subgroups within a specific subgroup

Published on 15 Apr 2026 - 2:16

114

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An Integer Linear Combinaton of Rationals is a Cyclic Group

Published on 11 Apr 2026 - 16:06

647

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$C_m \times C_n$ isomorphic to $C_{mn}$

Published on 29 Apr 2026 - 12:45

48

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Elements in the intersection of the groups

Published on 15 Apr 2026 - 9:02

329

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

Published on 29 Apr 2026 - 12:49

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How to find cyclic subgroup of group of permutations?

Published on 11 Apr 2026 - 22:08

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Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

Published on 14 Apr 2026 - 21:42

181

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Prove that for all elements $a$ of a group, $a^k a^l = a^{k+l}$ for all $k,l \in \mathbb{Z}$

Published on 15 Apr 2026 - 3:21

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Suppose that m ∈ Z≥1, Cm is a cyclic group of order m, and φ∶ Cm → Cm is an isomorphism. Prove that if a generates Cm then φ(a) generates Cm.

Published on 14 Apr 2026 - 23:29

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A question about cyclic group and Euler’s totient function

Published on 11 Apr 2026 - 7:18

1.4k

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Understanding cyclic groups with Cayley tables

Published on 21 Apr 2026 - 11:28

List Question

Show that the order of group $G$ is $1$ or a prime number

On a special type of finite abelian groups of prime power order

Transpositions and permutations algebraic proeprties

Group theory, subgroup of index 2

Number of subgroups within a specific subgroup

An Integer Linear Combinaton of Rationals is a Cyclic Group

$C_m \times C_n$ isomorphic to $C_{mn}$

Elements in the intersection of the groups

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

How to find cyclic subgroup of group of permutations?

Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

Prove that for all elements $a$ of a group, $a^k a^l = a^{k+l}$ for all $k,l \in \mathbb{Z}$

Suppose that m ∈ Z≥1, Cm is a cyclic group of order m, and φ∶ Cm → Cm is an isomorphism. Prove that if a generates Cm then φ(a) generates Cm.

A question about cyclic group and Euler’s totient function

Understanding cyclic groups with Cayley tables

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