# Minimum size of generating set of extension group is bounded by sum of minimum size of generating set of normal subgroup and quotient group

This article gives the statement, and possibly proof, of a group property (i.e., finitely generated group) satisfying a group metaproperty (i.e., extension-closed group property)
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## Statement

### Quantitative version

Suppose $G$ is a group, $H$ is a normal subgroup, and $G/H$ is the corresponding quotient group. If $a$ denotes the minimum size of generating set for $H$ and $b$ denotes the minimum size of generating set for $G/H$, then the minimum size of generating set for $G$ is at most $a + b$.

### Corollary for finitely generated groups

Suppose $G$ is a group, $H$ is a normal subgroup, and $G/H$ is the corresponding quotient group. Then, if both $H$ and $G/H$ are finitely generated groups, so is $G$.