Image-closed intermediately subnormal-to-normal subgroup

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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]

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Definition

A subgroup $H$ of a group $G$ is termed image-closed intermediately subnormal-to-normal in $G$ if, for any surjective homomorphism $\varphi :G\to K$, $\varphi (H)$ is an intermediately subnormal-to-normal subgroup of $K$.

This property was called strong transitively normal in a paper by Kurdachenko and Subbotin (see #References).

Formalisms

In terms of the image condition operator

This property is obtained by applying the image condition operator to the property: intermediately subnormal-to-normal subgroup
View other properties obtained by applying the image condition operator

Relation with other properties

Stronger properties

• Pronormal subgroup
• Weakly pronormal subgroup
• Paranormal subgroup
• Polynormal subgroup

Weaker properties

• Intermediately subnormal-to-normal subgroup
• Subnormal-to-normal subgroup

References

Journal references

• Transitivity of normality and pronormal subgroups by L. A. Kurdachenko and I. Ya. Subbotin, Combinatorial group theory, discrete groups, and number theory, Volume 421, Page 201 - 210(Year 2006): ^{More info}