... the set of all linear combinations of the elements of
S is a subgroup of Z, and its positive generator is the gcd of the elementsof S.
Exercise Show that the gcd of S = {90, 70, 42} is 2, and find ... Show the intersection of a collection of normal subgroups of G is a
normal subgroup of G. Show the union of a monotonic collection of normal subgroups
of G is a normal subgroup of G.
Exercise Let ... Define the gcd and the
lcm of the elementsof S and develop their properties. Express the gcd and the lcm
in terms of the prime factorizations of the a
i
. When is the lcm of S equal to the
product...
... contents
of certain cells escape in the form of large zoöspores (Fig. 16, C), of oval form, having
the smaller end colorless and surrounded by a crown of cilia. After a short period of
active ... produced, andof these tissues are built up the
various organs of the higher plants. The simplest tissues are rows of cells, such as
form the hairs covering the surface of the organs of many ... water and placed in a saucer filled with sand. A strip of blotting paper about the
width of the slide is now placed with one end in the water, the other hanging over the
edge of the glass and...