Q-group

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

Definition with symbols

A group $G$ is termed a Q-group if it has a subgroup $A$ satisfying the following:

• $A$ is Abelian but not elementary Abelian
• $A$ is a subgroup of index two in $Q$, hence normal
• There is an element $x\in G\setminus A$ such that $x^{2}$ is an element in $A$ of order two