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A problem with lemma about cyclic groups

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#abstract-algebra #group-theory #finite-groups #cyclic-groups
372
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Express a quotient of a free abelian group as a direct sum of cyclic groups

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#group-theory #abelian-groups #cyclic-groups #cyclic-decomposition
724
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Generator of a cyclic group under the operation $a\oplus b=(a+b+2)\bmod 5$

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#abstract-algebra #group-theory #cyclic-groups
55
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Groups with cyclic radicals

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#group-theory #cyclic-groups #torsion-groups
170
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What do the solvable groups in a free product of cyclic groups look like?

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#group-theory #cyclic-groups #solvable-groups #free-product
1.2k
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No Non trivial subgroup means prime order?

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#group-theory #cyclic-groups
1.9k
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Find out all the generators of the Cyclic group U17?

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#abstract-algebra #cyclic-groups
1.9k
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Does there exist non trivial group homomorphism from $S_3$ to ( $\mathbb Q $,+)

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#abstract-algebra #group-theory #rational-numbers #cyclic-groups #group-homomorphism
203
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Negative exponent of exponent in cyclic group of prime power order.

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#exponentiation #cyclic-groups
1.3k
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Show that every group of order $5865$ is cyclic

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#group-theory #cyclic-groups #sylow-theory #simple-groups
86
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Sampling random elements from a cyclic group

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#cyclic-groups
259
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The sum of elements in an abelian group doesn't equal 0 iff it's sylow-2 group is cyclic

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#group-theory #cyclic-groups #sylow-theory
95
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Find the order of $\operatorname {Aut}(C_p^{\oplus n})$

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#abstract-algebra #group-theory #cyclic-groups #automorphism-group
85
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About $ f(x) + c \space f(g(x)) = h(x) $

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#calculus #functional-equations #cyclic-groups
205
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The order of a group versus its cyclic subgroup

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#cyclic-groups

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