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Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.

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#abstract-algebra #group-theory #cyclic-groups
950
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union of proper subgroup is proper?

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#group-theory #finite-groups #cyclic-groups
131
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Why can't a group with more than p-1 elements be cyclic?

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#group-theory #finite-groups #cyclic-groups
1.9k
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Finding the other elements of order 8

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#abstract-algebra #finite-groups #cyclic-groups
75
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Roots of unity. Why is this function between $G_n$, $G_m$ bijective?

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#abstract-algebra #elementary-number-theory #cyclic-groups #roots-of-unity
328
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Showing the number of elements of certain order in an Automorphism of a group G

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#finite-groups #cyclic-groups #direct-product
203
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Proving that a Group isn't Cyclic

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#abstract-algebra #group-theory #cyclic-groups
56
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How can I combine $C_2$ with $C_2$ to obtain $C_4$?

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#group-theory #finite-groups #cyclic-groups
113
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Showing the external direct product of U group is not cyclic

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#finite-groups #cyclic-groups #direct-product
21
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computationally efficient way to determine the cube of a U-group is the U-group itself.

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#finite-groups #cyclic-groups #direct-product
574
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Find a subgroup of order 6 in U($700$)

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#group-theory #finite-groups #cyclic-groups #direct-product
798
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Showing there is a U-group containing a subgroup isomorphic to $Z_{14}$

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#finite-groups #cyclic-groups #direct-product
341
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Proving a Group is a Subgroup

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#abstract-algebra #group-theory #proof-writing #cyclic-groups
132
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Order of a factor group and whether it is cyclic

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#group-theory #finite-groups #cyclic-groups
2.5k
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Order of the elements in $Z_n$

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#abstract-algebra #cyclic-groups

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