A group $G$ is solvable if there exists a chain of subgroups \[ \langle e\rangle =H_0\leq H_1 \leq H_2 \leq \cdots \leq H_n=G\] such that for all $i<n$, $H_i$ is a normal subgroup of $H_{i+1}$ (i.e., it is a subnormal series) and each quotient $H_{i+1}/H_i$ is abelian.
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- Last edited by Jennifer Paulhus on 2022-07-19 08:58:08
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- columns.gps_groups.solvable
- columns.gps_subgroups.quotient_solvable
- columns.gps_subgroups.solvable
- group.abstract.432.734.bottom
- group.abstract.60.5.top
- group.alternating
- group.derived_series
- group.metabelian
- group.monomial
- group.nilpotent
- group.permutation_gens
- group.properties_interdependencies
- group.radical
- group.socle
- group.subgroup_properties_interdependencies
- group.supersolvable
- group.symmetric
- group.type
- modlgal.solvable
- lmfdb/galois_groups/main.py (line 120)
- lmfdb/galois_groups/main.py (line 446)
- lmfdb/galois_groups/main.py (line 539)
- lmfdb/galois_groups/templates/gg-show-group.html (line 98)
- lmfdb/groups/abstract/main.py (lines 266-267)
- lmfdb/groups/abstract/main.py (line 294)
- lmfdb/groups/abstract/main.py (lines 443-445)
- lmfdb/groups/abstract/main.py (line 1065)
- lmfdb/groups/abstract/main.py (line 1087)
- lmfdb/groups/abstract/main.py (line 1761)
- lmfdb/groups/abstract/main.py (line 2081)
- lmfdb/groups/abstract/main.py (line 2089)
- lmfdb/groups/abstract/stats.py (line 106)
- lmfdb/groups/abstract/stats.py (line 187)