input: Make use of the article to answer the questions. In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely. It allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics.

Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincare groups can express the physical symmetry underlying special relativity. 1. In math, what is a group called?
2. What pair is a group made of?
3. Does it merge any two to form a third?
4. How many conditions does it meet?
5. What are the four called?
6. Groups share a closeness with the notion of what?
7. What does a symmetry group encode features of?
8. What are point groups used to help figure out?
9. The ubiquity of groups in few areas?
10. What are group axioms?
11. Is it detached from the group?
numbered_answers: 1. An algebraic structure
2. Elements
3. Yes.
4. Four.
5. Group axioms
6. Symmetry.
7. A geometrical object:
8. Phenomena
9. Numerous.
10. Closure, associativity, identity and invertibility
11. Yes.

input: Make use of the article to answer the questions. Paul woke up at 8. He was very happy because today he got to go to his favorite thing, the fair. Paul's mother Beth was taking him to the fair. After finishing breakfast at 9, Paul got in the car with his mom. At 10 they got to Jim's house to pick him up. Jim was Paul's best friend. Then at 11, they picked up Beth's boyfriend Hank. After driving for one more hour they all finally got to the fair at 12. They had all been looking forward to this for a very long time. Beth was a bit annoyed by having to drive so much to get here, but she loved her son very much so the trouble was okay. Everyone had a great time, most of all, Paul. Gail's favorite ride was Ferris. Hank's favorite ride was the Ghoster. It was very scary. Paul's favorite ride was the same as Hank's. 1. who woke up?
2. when?
3. how did he feel?
4. why?
5. who took him?
6. was she married?
7. how long did it take to get there?
8. how many people were in the vehicle?
9. what did Paul do before getting in the vehicle?
10. how long was the trip to Jim's home?
11. did beth enjoy the trip to the fair?
12. how did she feel about her child?
13. did she like the fair?
14. did she like it the most?
15. what was hank's favorite?
16. did paul and gail like the same one?
17. what did she like?
18. who was jim?
numbered_answers: 1. Paul
2. at 8
3. very happy
4. the fair.
5. Paul's mother
6. No
7. 3 hours
8. Four
9. eat
10. 1 hour
11. No
12. she loved her son
13. Yes
14. No
15. the Ghoster
16. No
17. Ferris
18. Paul's best friend

input: Make use of the article to answer the questions. CHAPTER VIII

AFFAIRS OF LAULII AND FANGALII

_November--December_ 1888

For Becker I have not been able to conceal my distaste, for he seems to me both false and foolish. But of his successor, the unfortunately famous Dr. Knappe, we may think as of a good enough fellow driven distraught. Fond of Samoa and the Samoans, he thought to bring peace and enjoy popularity among the islanders; of a genial, amiable, and sanguine temper, he made no doubt but he could repair the breach with the English consul. Hope told a flattering tale. He awoke to find himself exchanging defiances with de Coetlogon, beaten in the field by Mataafa, surrounded on the spot by general exasperation, and disowned from home by his own government. The history of his administration leaves on the mind of the student a sentiment of pity scarcely mingled.

On Blacklock he did not call, and, in view of Leary's attitude, may be excused. But the English consul was in a different category. England, weary of the name of Samoa, and desirous only to see peace established, was prepared to wink hard during the process and to welcome the result of any German settlement. It was an unpardonable fault in Becker to have kicked and buffeted his ready-made allies into a state of jealousy, anger, and suspicion. Knappe set himself at once to efface these impressions, and the English officials rejoiced for the moment in the change. Between Knappe and de Coetlogon there seems to have been mutual sympathy; and, in considering the steps by which they were led at last into an attitude of mutual defiance, it must be remembered that both the men were sick,--Knappe from time to time prostrated with that formidable complaint, New Guinea fever, and de Coetlogon throughout his whole stay in the islands continually ailing. 1. who was weary ?
2. of what ?
3. what did they disire ?
4. what would they welcome ?
5. of what ?
6. who was found of smoma ?
7. was he famous ?
8. did the story teller like becker ?
9. why ?
10. and what else ?
11. who followed him ?
12. did he think he could fix something ?
13. what was it ?
14. with who ?
15. how had fever ?
16. and where was the stay ?
17. who was ready to wink ?
18. during what ?
19. how many atates are mentioned ?
20. name one ?
numbered_answers:
1. England
2. Samoa
3. peace
4. result
5. German settlement
6. Dr. Knappe
7. yes
8. no
9. seems to me both false
10. foolish
11. Knappe
12. yes
13. breach
14. English consul
15. New Guinea
16. islands
17. English consul
18. the process
19. Three
20. suspicion