-
finite group theory, the
Sylow theorems are a
collection of
theorems named after the
Norwegian mathematician Peter Ludwig Sylow that give
detailed information...
-
Peter Ludvig Meidell Sylow (Norwegian pronunciation: [ˈsyːlɔv]) (12
December 1832 – 7
September 1918) was a
Norwegian mathematician who
proved foundational...
- The
Sylow subgroups of the
symmetric groups are
important examples of p-groups. They are more
easily described in
special cases first: The
Sylow p-subgroups...
- of
primes in π, and
whose index is not
divisible by any
primes in π. Any
Sylow subgroup of a
group is a Hall subgroup. The
alternating group A4 of order...
-
Sylow-Tournament (Danish:
Sylow-Turneringen) was a
knockout ****ociation
football competition contested annually between 1918 and 1926,
organised by the...
-
Groups of 2-rank 2.
Alperin showed that the
Sylow subgroup must be dihedral, quasidihedral, wreathed, or a
Sylow 2-subgroup of U3(4). The
first case was done...
- (the
number of its elements) is a
power of p.
Given a
finite group G, the
Sylow theorems guarantee the
existence of a
subgroup of G of
order pn for every...
-
groups of
order n, as a consequence, for example, of
results such as the
Sylow theorems. For example,
every group of
order pq is
cyclic when q < p are...
-
phrased simply as "normalizers grow".
Every Sylow subgroup of G is normal. G is the
direct product of its
Sylow subgroups. If d
divides the
order of G, then...
- {\displaystyle G} it
suffices to
compute the
automorphism groups of the
Sylow p {\displaystyle p} -subgroups
separately (that is, all
direct sums of cyclic...
