Last Updated：2025/12/05
(algebra, Galois theory) A group which has a chain of subgroups going from itself all the way down to the trivial subgroup, such that any subgroup in the chain is a normal subgroup of the one immediately above it in the chain, and such that the quotient of any subgroup by the normal subgroup immediately under it is a cyclic group.
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solvable group
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Source Word
solvable group
Noun
(algebra,
Galois
theory)
A
group
which
has
a
chain
of
subgroups
going
from
itself
all
the
way
down
to
the
trivial
subgroup,
such
that
any
subgroup
in
the
chain
is
a
normal
subgroup
of
the
one
immediately
above
it
in
the
chain,
and
such
that
the
quotient
of
any
subgroup
by
the
normal
subgroup
immediately
under
it
is
a
cyclic
group.
Japanese Meaning
可解群：群自身から自明群までの部分群系列（鎖）が存在し、その系列において各部分群が直上の部分群に対して正規部分群であり、かつ連続する2群の商が巡回群となる群。
Sense（1）
(algebra,
Galois
theory)
A
group
which
has
a
chain
of
subgroups
going
from
itself
all
the
way
down
to
the
trivial
subgroup,
such
that
any
subgroup
in
the
chain
is
a
normal
subgroup
of
the
one
immediately
above
it
in
the
chain,
and
such
that
the
quotient
of
any
subgroup
by
the
normal
subgroup
immediately
under
it
is
a
cyclic
group.
（ plural ）
