Все публикации

0:04:37

f is homomorphism and if H is subgroup then f(H) is subgroup

0:00:57

f(g^n)=(f(g))^n for all n in Z

0:03:14

homomorphism carries identity on identity

0:03:46

Kernel is subgroup

0:06:48

If f(g) = g' then f^-1(g')= {xE G | f(x)=g'}= gKer f.

0:05:56

let f be homomorphism and if order of g=n then order of f(g) divides n

0:03:07

Kernel of homomorphism, definition and example

0:18:41

definition of homomorphism

0:13:04

G/Z theorem let Z(G) be the center of G. If G/Z(G) is cyclic, then G is Abelian.

0:05:50

Normal Subgroup Test A subgroup H of G is normal in G iff xHx'1 contained in H for all x in G.

0:10:16

Let G be a group and let Z(G) be the center of G. If G/Z(G) is cyclic, then G is Abelian.

0:10:44

Fermat’s Little Theorem in detail

0:07:54

Factor group definition

0:03:36

A subgroup H of a group G is called a normal subgroup of G if aH=Ha for all a in G.

0:16:41

Fermat’s Little Theorem

0:03:08

Corollary Let G be a finite group, and let a belongs to G. Then, a|G|= e.

0:04:00

Corollary -A group of prime order is cyclic.

0:03:46

Corollary |a| Divides |G|, the order of each element of the group divides the order of the group.

0:20:21

converse of Langranges theorem not true

0:07:14

Langranges Theorem-If G is a finite group and H is a subgroup of G, then |H| divides |G|

0:06:53

aH is a subgroup of G if and only if a belong to H

0:01:41

aH = Ha if and only if H = aH inverse(a)

0:04:02

number of elements in two left cosets are equal

0:06:09

aH=bH iff inverse(a)b belongs to H