Generalized dihedral group for 2-quasicyclic group

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group is defined as the generalized dihedral group corresponding to the 2-quasicyclic group.

Group properties

Property	Satisfied?	Explanation
p-group	Yes	p-group for $p=2$.
abelian group	No
centerless group	No	The center has order two.
locally finite group	Yes
Artinian group	Yes
hypercentral group	Yes	See locally finite Artinian p-group implies hypercentral
locally nilpotent group	Yes
nilpotent group	No
residually nilpotent group	No
metabelian group	Yes
solvable group	Yes
finite group	No
finitely generated group	No
countable group	Yes