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 $\phi :G\to K$, $\phi (H)$ 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

1. 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}