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0:26:25
A permutation is a cycle or product of disjoint cycles
0:24:43
Permutation group
0:15:29
cycle notation, order of cycle
0:09:26
If d is positive divisor of n then number of elements of order d in (a) is phi(d)group theory gallia
0:09:26
If d is positive divisor of n then number of elements of order d in (a) is phi(d)
0:11:18
for each positive divisor k of n, the group (a) has exactly one subgroup of order k
0:13:30
If order of a cyclic group is n, then order of every subgroup is divisor of n
0:21:25
Every subgroup of a cyclic group is cyclic, fundamental th. of algebra
0:47:15
Fundamental theorem of algebra
0:05:02
corollary: Let G be a group and a belongs to G with o(a)=n and if a*k=e then n/k
0:18:44
Let G be cyclic group of order n then a_k is generator of G if gcd(k, n)=1
0:06:35
let G be a group and a belong to a to G has infinite order, then all distinct power of the a are
0:24:14
symmetric group of squares
0:14:31
cyclic group, order of group and example
0:14:23
General Linear group of invertible matrices, GL(2, Z7) is a group,
0:11:42
Let H be nonempty finite subgroup of group G then H is subgroup if it is closed
0:07:21
Let G be an ablian group then H containing elements of whose square is identity is subgroup
0:03:25
2Z is subgroup of Z under addition
0:09:54
example of order of group and elements of group
0:08:35
Inverse of a matrix in GL(2,Z11)
0:24:33
definition of congruence modulo and example
0:11:17
Order of group and elements
0:05:38
In a group inverse of ab=inverse of b inverse of a
0:03:10
inverse of inverse a= a
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