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Uncommon card · Science
Galois group, an Uncommon card
In Galois theory, a branch of abstract algebra, the Galois group of a certain type of field extension is a symmetry group characterizing how it extends the base field.
- Rarity
- Uncommon
- Domain
- Science
- ATK
- 64
- DEF
- 38
- Power
- 102
- Wikipedia reads a year
- 68,000
Power 102 (ATK + DEF): stronger than 55 % of WikiCards cards.
Galois group quiz: 3 questions
Three questions on the Galois group card, the way WikiCards duels ask them. Pick an answer, the facts are just below.
Find the missing word
Each element of the Galois group is a ______ of the field extension which leaves each element of the base field fixed.
Answer
transformation. Each element of the Galois group is a transformation of the field extension which leaves each element of the base field fixed. From the Galois group article on Wikipedia.
Which of these cards hits hardest (highest ATK)?
Answer
Numeral system. Numeral system 69 · Galois group 64 · Perlin noise 60 · Brocade 55 ATK in WikiCards.
Which of these Wikipedia articles is read the most in a year?
Answer
Numeral system. Numeral system 170,000 · Brocade 98,000 · Galois group 68,000 · George Smith 54,000 Wikipedia reads over a year.
In a duel, each round asks a question like these about the opposing card, with 15 seconds to answer.
The facts on the card
The card carries these facts from its Wikipedia article.
- Each element of the Galois group is a transformation of the field extension which leaves each element of the base field fixed.
- This connection between fields and groups, given by the fundamental theorem of Galois theory, allows for group-theoretic tools to be used on problems in field theory, such as describing the solutions to quintic polynomials.
- The study of field extensions and their relationship to the polynomials that give rise to them via Galois groups is called Galois theory, so named in honor of Évariste Galois who first discovered them.
Why it is Uncommon
Rarity in WikiCards follows a year of Wikipedia page views: the most read articles become Epic and Legendary cards. The Galois group article was read about 68,000 times in a year. ATK comes from the length of the article and DEF from its quality, so this card hits with 64 and blocks with 38: each hit it takes is cut by 15 %.
How to get Galois group
Open packs. Each pack holds five cards drawn from real Wikipedia articles, the rarest last, and the fifth card is always Rare or better. The odds are shown in the game. A free pack arrives every hour and two can wait, and the Coins you win in duels buy more packs.
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Credits
Text : Wikipedia, Galois group (revision), CC BY-SA 4.0. Photo : Self, CC BY-SA 3.0, Wikimedia Commons.
