- In mathematics, an
element x {\displaystyle x} of a ring R {\displaystyle R} is
called nilpotent if
there exists some
positive integer n {\displaystyle...
-
forms of the
definition of
nilpotency, that the
trivial group is the
unique group of
nilpotency class 0, and
groups of
nilpotency class 1 are
exactly the...
- doi:10.2307/1971440, JSTOR 1971440, MR 0960945 Nishida, Goro (1973), "The
nilpotency of
elements of the
stable homotopy groups of spheres",
Journal of the...
-
nilpotency class n − 1, and are the only
isomorphism classes of
groups of
order 2n with
nilpotency class n − 1. The
groups of
order pn and
nilpotency...
- the 2-groups of
maximal class, that is
those groups of
order 2n+1 and
nilpotency class n. The
iterated wreath products of
cyclic groups of
order p are...
-
diagonalizable matrix is the zero matrix. See also: Jordan–Chevalley decomposition#
Nilpotency criterion.
Consider the n × n {\displaystyle n\times n} (upper) shift...
- (x_{n})=\pi (x)_{n}} . The
Jordan decomposition can be used to
characterize nilpotency of an endomorphism. Let k be an
algebraically closed field of characteristic...
-
problem in
finite group theory which had
stood for
around sixty years: the
nilpotency of
Frobenius kernels. At the time, this
achievement was
noted in The New...
- group.
Frobenius groups whose ****ing
subgroup has
arbitrarily large nilpotency class were
constructed by Ito: Let q be a
prime power, d a
positive integer...
- we will not
prove here. A
somewhat easier equivalent condition for the
nilpotency of g {\displaystyle {\mathfrak {g}}} : g {\displaystyle {\mathfrak {g}}}...
