If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G is: *

Q: Let G be a finite group of order n. Let g be an element of G. Prove that gn=e.

A:

Q: 3. Let G be a group, H a subgroup of G, and g and element of G. (a) Prove that {ghg-1 | h e H} is…

A: Let G be a group, H is a subgroup of G, and g be an element of G

Q: G. Show that if H and K are subgroups of an abelian group G, then {hk\h E H andke K} is a subgroup…

A:

Q: Let G be a finite cyclic group and a be an element of G of order 8 then the order of G would be: O…

A:

Q: 5. Let p and q be two prime numbers, and let G be a group of order pq. Show that every proper…

A: We have to prove that: Every proper subgroup of G is cyclic. Where order of G is pq and p , q are…

Q: Let G be a finite cyclic group and a be an element of G of order 8 then the order of G would be

A: Would be a group.

Q: Let G be a group of order 42. Find all possible orders |H| for a subgroup H of G, and in each case…

A:

Q: If G is a finite group with |G|<160 and G has subgroups of orders 1O, 16 and 20 then the order of G…

A:

Q: Let H be a subgroup of a group G and a, b E G. Then be aH if and only if *

A: So,  a, b  belongs to H, and we have  b∈aH  Hence,  b = ah     -- for some element of H  Hence,  a-1…

Q: Let G be a finite group and H1, H2,…., Hk be subgroups of G. .... (a) Show that N H; = Hị n H2 n..n…

A:

Q: Suppose H and K be subgroups of a finite group G with |G : H| = m and |G : K| = n. Prove that…

A: We use here, Tower law of subgroup which states that Let (G,∘) be a group.  Let H be a subgroup of G…

Q: If H is a normal subgroup of a finite group G and |H| = pk for someprime p, show that H is contained…

A: H is a normal subgroup of a finite group G and |H| = pk for some prime p.

Q: Let G be an abelian group and suppose that H and K are subgroups of G. Show that the following set…

A: According to the given information, Let G be an abelian group and suppose that H and K are subgroups…

Q: Let G be a finite group and H a subgroup of G of order n. If H is the only subgroup of G of order n,…

A: Given, G is a finite group and H is a subgroup of G of order n.

Q: Let G be a group with |G|=187 then every proper subgroup of G is:

A:

Q: Suppose S is a nonempty subset of a group G.(a) Prove that if S is finite and closed under the…

A: (a)Suppose S is a non-empty subset of a group G. then we have to prove that if S is finite and…

Q: If G is a finite group with |G|<120 and G has subgroups of orders 1O, 15 and 20 then the order of G…

A: Using Lagrange's theorem it can be written that if G is a finite group and B is a subgroup of G,…

Q: If G is a finite group, H ≤ G, the order of H divides the order of G: | H | / | G | Prove

A:

Q: Let G be a finite group. Let x E G and let G be the conjugacy class of r. Prove that |#C| < |[G,…

A: Given G be a finite group. Let x∈G. Define: xG=gxg-1: g∈G Let G:G=m. Define a map π:G→GG:G defined…

Q: If G is a finite group with |Gl<120 and G has subgroups of orders 10, 15 and 20 then the order of G…

A: Given: The group G is a finite group with | G | &lt; 120 and G has subgroups of orders 10, 15, and…

Q: Let G be a group and let H and K subgroup of G. Prove that the intersection H and K is a subgroup of…

A:

Q: Let G be a finite group. Let E G and let xG be the conjugacy class of x. Prove that x| < |[G, G]],…

A:

Q: An element a of a group G has order n E z+ if and only if a" = e.

A: The given statement is False.

Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G…

A:

Q: Give an example of a finite group G with two normal subgroups H and K such that G/H = G/K but H 7 K.

A:

Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 ano then the order of G is:…

A:

Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G…

A:

Q: 4. Let H be a subgroup of a group G. Show that exactly one left coset of H is a subgroup.

A:

Q: Suppose that G is a cyclic group such that Ord(G) = 54. The number of subgroups that G has is * 10…

A: If G is cyclic group and order of G is 'n'. Then number of subgroups of G is equal to number of…

Q: If G is a finite group with |G|<180 and G has subgroups of orders 10, 18 and 30 then the order of G…

A:

Q: Let G be a group with p or more distinct elements of order p for some prime p. Show that G is not…

A: Given : Let G be a group which has p  elements of order p, p is a prime no.  To show G is not cyclic…

Q: If G is a finite group with IG|<120 and G has subgroups of orders 10, 15 and 20 then the order of G…

A:

Q: If G is a finite group with IG|<160 and G has subgroups of orders 10, 16 and 20 then the order of G…

A: Given :- order of a group G... |G| &lt; 160 Also order of subgroups of group G are 10, 16 , 20. We…

Q: Let G be a finite cyclic group and a be an element of G of order 8 then the order of G would be: 2…

A:

Q: If G is a finite group with IG|<120 and G has subgroups of orders 10, 15 and 20 then the order of G…

A: Using Lagrange's theorem it can be written that if G is a finite group and A is a subgroup of G,…

Q: Let G be a finite cyclic group and a be an element of G of order 9 then the order of G would be: * 4…

A: Fourth option is correct.

Q: A subset of H of a group G is a subgroup of G if the operation on G makes H into a group. Prove that…

A:

Q: If G is a finite group with |G|<180 andG has subgroups of orders 10, 18 and 30 then the order of G…

A: Use the fact that order of subgroup divides order of group

Q: If H is the subgroup of group G where G is the additive group of integers and H = {6x | x is the…

A: Let H is a subgroup of order 6 . Take H=6Z where Z is integers.

Q: G is a finite group of order IGI =pqr with p< q <r prime

A: Solution

Q: If G is a cyclic group, prove for subgroup N that G is a cyclic N

A:

Q: Let G be a finite group and let H be a normal subgroup of G. Provethat the order of the element gH…

A: Given: G be a finite group and H be a normal subgroup of G.

Q: Suppose that G is a cyclic group such that Ord(G) = 54. The number of subgroups that G has is * 10 O…

A:

Q: 3. Let G be a finite group with an odd number of elements. Prove that G is isomorphic to a subgroup…

A:

Q: 2. Let G be a group of order /G| = 49. Explain why every proper subgroup of G is сyclic.

A:

Q: Let H and K be subgroups of a finite group G. Show that |HK |HK= |HОКI where HK (hk hE H, k E K}.…

A: let D = H ∩K then D is a subgroup of k and there exist a decomposition of k into disjoint right…

Q: If G is a finite group with |G|<120 and G has subgroups of orders 10, 15 and 20 then the order of G…

A:

Q: Let G be a group with no proper, nontrivial subgroups and assume that |G| > 1. Prove that G must be…

A:

Q: 6. Let G be a group of order p², where p is a prime. Show that G must have a subgroup of order p.

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.