- have
infinite order. The
subgroups of any
given group form a
complete lattice under inclusion,
called the
lattice of
subgroups. (While the
infimum here...
-
algebraic groups.
Subgroups between a
Borel subgroup B and the
ambient group G are
called parabolic subgroups.
Parabolic subgroups P are also characterized...
-
congruence subgroup problem,
which asks
whether all
subgroups of
finite index are
essentially congruence subgroups.
Congruence subgroups of 2 × 2 matrices...
-
given generalized ****ing
subgroup. The
normalizers of
nontrivial p-
subgroups of a
finite group are
called the p-local
subgroups and
exert a
great deal of...
-
Subgroup analysis refers to
repeating the
analysis of a
study within subgroups of
subjects defined by a
subgrouping variable. For example:
smoking status...
- of G, but G has no
subgroups of
these orders. The
simple group of
order 168 has two
different conjugacy classes of Hall
subgroups of
order 24 (though...
-
group then its
unique maximal subgroup (as a semigroup) is S itself.
Considering subgroups, and in
particular maximal subgroups, of
semigroups often allows...
-
subgroups are
important because they (and only they) can be used to
construct quotient groups of the
given group. Furthermore, the
normal subgroups of...
- {\displaystyle p} -
subgroup of G {\displaystyle G} is a
normal subgroup. However,
there are
groups that have
normal subgroups but no
normal Sylow subgroups, such as...
- group. (cf. Hilbert's
fifth problem.) Hilbert's
fifth problem § No
small subgroups M. Goto, H., Yamabe, On some
properties of
locally compact groups with...
