Characteristically simple implies CSCFN-realizable: Difference between revisions
(New page: {{group property implication| stronger = characteristically simple group| weaker = CSCFN-realizable group}} ==Statement== Any characteristically simple group can be realized as a [[f...) |
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# [[Characteristically simple and NSCFN implies monolith]] | # [[Characteristically simple and NSCFN implies monolith]] | ||
# [[Monolith is characteristic]] | # [[Monolith is characteristic]] | ||
==Proof== | |||
The proof follows from facts (1)-(4). | |||
Revision as of 21:12, 2 September 2009
This article gives the statement and possibly, proof, of an implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., characteristically simple group) must also satisfy the second group property (i.e., CSCFN-realizable group)
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Get more facts about characteristically simple group|Get more facts about CSCFN-realizable group
Statement
Any characteristically simple group can be realized as a CSCFN-subgroup (?) of some group.
Facts used
- Characteristically simple implies center is a direct factor
- Center is a direct factor implies NSCFN-realizable
- Characteristically simple and NSCFN implies monolith
- Monolith is characteristic
Proof
The proof follows from facts (1)-(4).