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Prove $\exists (u,v) \in \mathbb{Z}_n \times \mathbb{Z}_n$ st every element equals $k_1(a,b) + k_2(u,v)$

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#linear-algebra #number-theory #finite-groups #cyclic-groups
41
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Cyclic subgroup in the $\operatorname{SL}(n,\mathbb Z)$?

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#abstract-algebra #cyclic-groups
1.9k
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What are the units of $\mathbb Z/2\mathbb Z \times \mathbb Z/5\mathbb Z$

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#abstract-algebra #group-theory #ring-theory #cyclic-groups #direct-product
119
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A permutation of $\mathbb{Z}/n\mathbb{Z}$ disturbing distances is a group homomorphism?

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#permutations #cyclic-groups #group-homomorphism
65
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Abstract algebra, order of element

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#abstract-algebra #cyclic-groups
318
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Abelian group of order 155

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#group-theory #abelian-groups #cyclic-groups
91
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For generator $g$ of multiplicative group: if $\log_g (f^3) = 3x$, then $\log_g (f) = x$?

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#group-theory #finite-groups #cyclic-groups #discrete-logarithms
1.9k
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Order of cyclic subgroups in symmetric groups

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#group-theory #symmetric-groups #cyclic-groups
714
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Calculate Smith normal form, cyclic group decomposition

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#linear-algebra #abstract-algebra #cyclic-groups #cyclic-decomposition #smith-normal-form
527
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Uniqueness of group given only group presentation

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#abstract-algebra #group-theory #cyclic-groups #group-presentation
227
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Finding the generator set of a group

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#group-theory #cyclic-groups #finitely-generated
1.8k
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Find generator of multiplicative group of $\mathbb{F}_{27}$

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#finite-fields #cyclic-groups
441
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Cyclic multiplicative group and quadratic residues

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#group-theory #number-theory #cyclic-groups
39
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How to analyse congruence equations?

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#abstract-algebra #cyclic-groups
61
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How to tell if a group under multiplication is cyclic?

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#abstract-algebra #group-theory #cyclic-groups

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