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Essential subgroups and essential extensions
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DOI：10.1142/s0219498827502264.png)
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Abstract
En 中文
The notion of essential submodules and essential extensions of modules are extended to groups (typically nonabelian), and several necessary and sufficient conditions for a group to possess a proper essential subgroup are investigated. Further, we have completely characterized groups that do not possess a proper essential extension. These observations are used in concluding several properties of groups having essential subgroups. Finally, a short proof of the well-known theorem of Eilenberg and Moore that the only injective object in the category of groups is the trivial group is given.
Keywords:
Essential subgroup
essential extension
complete group
injective object in groups
extensional object
holomorph of a group
free product of groups
central product of groups
semi-direct product of groups
malnormal subgroup
group extensions
Journal
J
IF:
0.6
Papers:
261
Citations:
0
Organization
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