# Polynomial-bound join-transitively subnormal subgroup

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
If the ambient group is a finite group, this property is equivalent to the property: subnormal subgroup
View other properties finitarily equivalent to subnormal subgroup | View other variations of subnormal subgroup |
This is a variation of join-transitively subnormal subgroup|Find other variations of join-transitively subnormal subgroup |

## Definition

### Definition with symbols

A subgroup $H$ of a group $G$ is termed polynomial-bound join-transitively subnormal in $G$ if there exists a polynomial $f$ with integer coefficients such that if $K$ is a $k$-subnormal subgroup of $G$, $\langle H, K \rangle$ (the join of subgroups) is a $f(k)$-subnormal subgroup of $G$.

Here, a $k$-subnormal subgroup is a subgroup whose subnormal depth is at most $k$.