Flashcards
Math Final True/False
Flashcards do conjunto (78)
- 1The rational numbers under addition are a groupTrue
- 2The rational numbers under addition are abelianTrue
- 3The rational numbers under multiplication are a groupFalse, There is no inverse
- 4The rational numbers minus zero are a groupTrue
- 5The rational numbers minus zero are abelianTrue
- 6GL(2,R) under multiplication are a groupTrue
- 7GL(2,R) under multiplication are abelianFalse
- 8For the integers under addition, the negative integers are a subgroupFalse, not closed under inverse
- 9For the D4 group, (e,H) is a subgroupTrue
- 10For the D4 group, elements with order 2 are a subgroupFalse, not closed under operation
- 11Suppose a,b,c elements of Z. Then a|(b+c) and a|(b-2c) implies a|cFalse, a=3 b=10 c=-4
- 12If a is a positive integer then for all b,c elements of Z if a|bc then a|b or a|cFalse, a=6 b=3 c=2 (True for prime numbers)
- 13In any group, is s,t are elements of the group ans s^2=t^2 then s=tFalse, in D4 H^2=e and R180^2=e
- 14If a,b are elements of a group, then (ab)-1 = b-1a-1True, socks and shoes property
- 15If G is a group and a is an element of G ans a^4=e than the order of a is 4False, a=e
- 16Suppose s,t are integers, than there exists u,v subgroup of Z such that su+tv=2, than gcd(st)=2False, s=8, u=2, t=-7, v=2
- 17If G is a group, and a,b are elements of G, than aba-1=e than b=eTrue
- 18The order of Dn is nFalse, 2n
- 19The order of Z/521Z is 521True
- 20G is a group and a is an element of G. The order is a is 3. Than a^91 is eFalse, a^91 is a
- 21If n is an element of the natural numbers and a is an element of the integers, a mod n = 1 than gcd(a,n)=1True
- 22In Z/nZ if n>1 than the inverse of n is 1False, n-1
- 23There exists an element in A6 with order 4True, (1234)(56)
- 24There does not exist an element in S5 such that squaring it is not in A5True, the identity is in A5
- 25There does not exist an element in S7 with order 10False, (12)(34567)
- 26the order of (23)(45) is 4False, 2
- 27the order of (234)(15) is 6True
- 28(234)(15) can be written as a product of 2 cycles (23)(34)(15)False, (23)(24)(15)
- 293 elements in Z2(x)S3 have order 3False, 2
- 30if a,b are elements of a group with order 5 than the order of bab-1 is 5True
- 31if a,b are elements of a group with order 5 than the order of (bab-1)^2 is 5True
- 32If a is an element of G than the order of a divides the order of GTrue, Cor. of Lagrange's theorem
- 33If d is a positive integer and d||G| then there is a subgroup of G with order dFalse
- 34If the order of G is a prime number, than G is cyclicTrue
- 35The order of Sn is nFalse, n!
- 36The order of An is n!False, n!/2
- 37(12)(34) has order 2True
- 38Suppose G is a group and the order of G is 70 if the order of H is 10 a subgroup of G than there are 10 left co-setsFalse, 7
- 39The generators of Z10 are (e,9)False, (0,1,3,7,9)
- 40For any finite group G, with subgroup H and b element of G than bH=HbFalse, b must also be an element of H
- 41For any finite group G, with subgroup H and b element of G the order of bH is the order of HbTrue
- 42For any finite group G, with subgroup H and b element of G, the order of H is equal to the order of bHTrue
- 43Z5 has no elements of order 3True
- 44Z5(x)Z5 has no elements of order 25True
- 45b element of Z5-(0), than =Z5True
- 46Every non empty subset of Z contains a smallest elementTrue
- 47For any n element of the natural numbers in the groun Z/nZ if a is an element than a+a+a=0 than a+a=0False, In Z6 2+2+2=0 but 2+2=4
- 48In a group G with elements a,b of G is (ab)^2=a2b2 than ab=baTrue
- 49In Z/9Z, 5+7=5False, 3
- 50In D4, if a is an element of D4 and a is a reflection than a^521 is eFalse a
- 51If a subset X subset of the Reals, contains a smallest element than X satisfies the well ordering principalTrue
- 52Every finite subset of R satisfies the well ordering principalTrue
- 53Suppose a is a prime number. Then any b,c subset of Z. If a|bc than a|b or a|cTrue
- 54IF G is an Abelian group, than every subgroup of G is a normal subgroupTrue
- 55If G is a group and H is Abelian subgroup of G, then H is normal in GFalse, Let H=<(12)> in S3. It is abelian but not normal
- 56If G is a finite group, and N is a normal subgroup of G then the order of the factor group G/N divides the order of GTrue, |G/N|=|G|/|N|
- 57GL(2,R)/SL(2,R) is isomorphic to the group R-(0) under additionFalse, under multiplication
- 58The list of all generators of the the cyclic group Z2(X)Z3 are (1,1) and (1,2)True, pairs are (a,b) where a is a generator of the first and b is a generator of the second
- 59For n>3 Sn/An is isomorphic to ZnFalse, Z2
- 60An is normal in SnTrue
- 61A4 is not isomorphic to D6True A4 has no element in D6
- 62[-17,infinity]U Z satisfies the well ordering principalTrue
- 63[5,6] satisfies the well ordering principalFalse, (5,6)
- 64For all negative integers z, z|0True
- 65If z is an element of Z-(0) than |z||zTrue
- 66For any n element of N and a,b,c element of Z/nZ if a+b=a+c than b=cTrue
- 67For all n element of N in Z/nZ if a+a=0 than a=0False, in Z/6Z 3+3=0
- 68The cyclic subgroup is abelianTRUE
- 69If H is a non empty subset of G and H is closed under the operation then H is a subgroup of GFalse Integers under multiplication
- 70the inverse of (12) is (21)True
- 71S6 has an element of order 8False
- 72S4 has an element of order 5False
- 73A5 has elements of order 4False
- 74The number of elements of S4 of order 3 are 8True, 4!/3 = 8
- 75<(12)> is a normal subgroup of S4False, just a subgroup
- 76A4 is a normal subgroup of S4True
- 77H is a subgroup of G and a is an element of G and aH not equal to H, than aH is a subgroup of GFalse, than a is not an element of H
- 78H=<(12)> and K=<(23)> is HK is a subgroup of S3False
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- FlashCards sobre Math Final True/False, criado por amsond01 em 08-12-2015.
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- amsond01
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