Answer:
Step-by-step explanation:
We are given that G be a finite group with
have two elements of order two.
We have to prove that <x,y> is either abelian or isomorphic to a dihedral group.
<x,y> means the group generated by two elements of order 2.
We know that
is a cyclic group and number of elements of order 2 is always odd in number and generated by one element .So , given group is not isomorphic to ![Z_n](https://tex.z-dn.net/?f=Z_n)
But we are given that two elements of order 2 in given group
Therefore, group G can be
or dihedral group
Because the groups generated by two elements of order 2 are
and dihedral group.
We know that
is abelian group of order 4 and every element of
is of order 2 except identity element and generated by 2 elements of order 2 and dihedral group can be also generated by two elements of order 2
Hence, <x,y> is isomorphic to
or
.
Answer:
12 in. 2
Step-by-step explanation:
3 x 8= 24
1/2. =0.5
24 x 0.5 = 12
Answer:
y= -1/4 x -1
Step-by-step explanation:
slope intercept equation= y=mx+b
m= slope
b= y-int.
y-int= -1 (seen on graph)
b= -1
y=mx-1
slope is rise over run
-1/4
m= -1/4
y=-1/4x-1