# Let G be a group and a is an element of G. Prove that the cyclic group generated by a is a subgroup of G.?

• Let G be a group and a is an element of G. Prove that the cyclic group generated by a is a subgroup of G.?

Cyclic groups Lemma 4.1. Let Gbe a group and let H i, ... generated by one element. Let G= haibe a cyclic group. By ... Let Gbe a cyclic group, generated by a.
Positive: 99 %
Cyclic Groups. A group G is cyclic if ... by the order of g. Let be a cyclic group of ... subgroup generated by g is If the group is abelian and ...
Positive: 96 %

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Cyclic Groups Let G be a group and a G ... is called the cyclic subgroup of G generated by ... number of generators of a finite cyclic group. Let G = a ...
Positive: 99 %
... group $G$ of even order contains an element ... even order contains an element of order $2.$[ Let ... Prove that the order of the cyclic subgroup ...
Positive: 94 %
Answer to Let a and b be elements of a finite group G ... Prove that a subset H of a finite group G is a subgroup ... If G is a cyclic group, prove ...