0
The order of a group is the same as its cardinality - i.e. the number of elements the set contains. The order of a particular element is the order of the (cyclic) group generated by that element - i.e. the order of the group {...a-4, a-3, a-2, a-1, e, a, a2, a3, a4...}. If these powers do not go on forever, it will have a finite order; otherwise the order will be infinite.
Add your answer:
Earn +20 pts
What is the order of an element of a group?
The order of a group is the same as its cardinality - i.e. the number of elements the set contains. The order of a particular element is the order of the (cyclic) group generated by that element - i.e. the order of the group {...a-4, a-3, a-2, a-1, e, a, a2, a3, a4...}. If these powers do not go on forever, it will have a finite order; otherwise the order will be infinite.
What are the symbols of permutation groups?
some examples of symbols for permuation groups are: Sn Cn An These are the symmetric group, the cyclic group and the alternating group of order n. (Alternating group is order n!/2, n>2) One other is the Dihedral group Dn of order 2n.
Is a group of order 24 abelian group or not?
The abelian groups of order 24 are C3xC8, C2xC12, C2xC2xC6. There are other 12 non-abelian groups of order 24
To find the median does the group of number have to be put in numerical order?
No
The number of subgroups of order 25 in a group of order 200 is?
200_c_25 = 200!/(25!*(200-25)!) = 200!/(25!*175!) = 45217131606152448808778187283008
How many elements in group will have the order equal to the order of group?
Number of generators of that group
How many subgroup of a group of order 60 andorder 51?
how many subgroup of a group of order 60 and order 51?
What is the order of an element of a group?
The order of a group is the same as its cardinality - i.e. the number of elements the set contains. The order of a particular element is the order of the (cyclic) group generated by that element - i.e. the order of the group {...a-4, a-3, a-2, a-1, e, a, a2, a3, a4...}. If these powers do not go on forever, it will have a finite order; otherwise the order will be infinite.
What is the order of an element in a group?
The order of an element in a multiplicative group is the power to which it must be raised to get the identity element.
Where is the order group located today?
in the order of opration's
What is the order of the cyclic group mean?
The order of a cyclic group is the number of distinct elements in the group. It is also the smallest power, k, such that xk = i for all elements x in the group (i is the identity).
When was New Order - Neo-Nazi group - created?
New Order - Neo-Nazi group - was created in 1983.
What are the symbols of permutation groups?
some examples of symbols for permuation groups are: Sn Cn An These are the symmetric group, the cyclic group and the alternating group of order n. (Alternating group is order n!/2, n>2) One other is the Dihedral group Dn of order 2n.
Prove that a group of order three is abelian?
By LaGrange's Thm., the order of an element of a group must divide the order of the group. Since 3 is prime, up to isomorphism, the only group of order three is {1,x,x^2} where x^3=1. Note that this is a finite cyclic group. Since all cyclic groups are abelian, because they can be modeled by addition mod an integer, the group of order 3 is abelian.
What vertebrate group is a rat in?
The vertebrate group of rats is the order: Rodentia.
What is the next sub-group in classification class order?
The next sub-group in classification class order is family.
How do you create a group?
You have to have companions in order to 'create' a group. For example,One direction is a music group.Europe is a group of countries.You simply need over 1 person in order to create a group. I hope this helps.
