Properties of a group
How can we say that the pair (G, o) is a group. Explain the properties which proof it.
Expert
Let G be a set and suppose that o is a binary operation on G. We say that the pair (G; o) is a group if it has the following properties.
(i) The operation o is associative; that is, (g o h) o k = g o (h o k) for all g; h; k ≡ G.(ii) There exists an identity for o ; that is, there exists e ≡ G such that g o e = e o g = g for all g ≡ G.(iii) There exist inverses for o ; that is, for each g ≡ G, there exists g-1≡ G such thatg o g-1 = g-1 o g = e:There is another property implicit in this denition which it is useful to give a name to. Instead of saying that o is a binary operation on G, we can say that the law of closure holds for o, meaning that when o acts on two elements of G the result is also in G.
Most of the groups (G; o) we study will also have the following property.
(iv) The operation o is commutative; that is, g o h = h o g for all g; h ≡ G.
A group with this property is called commutative or, more usually, abelian, after the Norwegian mathematician Niels Henrik Abel (1802{1829).
Factorisation by Fermat's method: This method, dating from 1643, depends on a simple and standard algebraic identity. Fermat's observation is that if we wish to nd two factors of n, it is enough if we can express n as the difference of two squares.
this assignment contains two parts theoretical and coding the code has to be a new. old code and modified code will appear in the university website .
It's a problem set, they are attached. it's related to Sider's book which is "Logic to philosophy" I attached the book too. I need it on feb22 but feb23 still work
XYZ Company collects 20% of a month's sales in the month of sale, 70% in the month following sale, and 5% in the second month following sale. The remainder is not collectible. Budgeted sales for the subsequent four months are:
Select a dataset of your interest (preferably related to your company/job), containing one variable and atleast 100 data points. [Example: Annual profit figures of 100 companies for the last financial year]. Once you select the data, you should compute 4-5 summary sta
AB Department Store expects to generate the following sales figures for the next three months:
Anny, Betti and Karol went to their local produce store to bpought some fruit. Anny bought 1 pound of apples and 2 pounds of bananas and paid $2.11. Betti bought 2 pounds of apples and 1 pound of grapes and paid $4.06. Karol bought 1 pound of bananas and 2
8. Halloween is an old American tradition. Kids go out dressed in costume and neighbors give them candy when they come to the door. Spike and Cinderella are brother and sister. After a long night collecting candy, they sit down as examine what they have. Spike fi
Prime number theorem: A big deal is known about the distribution of prime numbers and of the prime factors of a typical number. Most of the mathematics, although, is deep: while the results are often not too hard to state, the proofs are often diffic
The augmented matrix from a system of linear equations has the following reduced row-echelon form.
18,76,764
1941986 Asked
3,689
Active Tutors
1442008
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!