Question

In: Advanced Math

Use the Sylow theorems to show (a) there are no simple groups of order 55 (b)...

Use the Sylow theorems to show

(a) there are no simple groups of order 55
(b) there are no simple groups of order 56

Solutions

Expert Solution

if you are not satisfied with this answer please don't thumb down. Thanks


Related Solutions

derive all groups of order 12 using sylow theorems. please dont use any generalizations show all...
derive all groups of order 12 using sylow theorems. please dont use any generalizations show all work and theorems used. all 5 of them
Show that the groups of the following orders have a normal Sylow subgroup. (a) |G| =...
Show that the groups of the following orders have a normal Sylow subgroup. (a) |G| = pq where p and q are primes. (b) |G| = paq where p and q are primes and q < p. (c) |G| = 4p where p is a prime greater than four.
Show that the normalizer of a 5-Sylow subgroup of A_5 has order 10, and is a...
Show that the normalizer of a 5-Sylow subgroup of A_5 has order 10, and is a maximal subgroup of A_5.
Identify three (3) theorems of plastics collapse and show the relationship of those theorems with the...
Identify three (3) theorems of plastics collapse and show the relationship of those theorems with the plastics load factor
Find a p-Sylow subgroup for each of the given groups, and prime p: a. In Z24...
Find a p-Sylow subgroup for each of the given groups, and prime p: a. In Z24 a 2-sylow subgroup b. In S4 a 2-sylow subgroup c. In A4 a 3-sylow subgroup
show that if H is a p sylow subgroup of a finite group G then for...
show that if H is a p sylow subgroup of a finite group G then for an arbitrary x in G x^-1 H x is also a p sylow subgroup of G
prove groups of order 12,24,36, and 48 arent simple. i want discrete cases if possible not...
prove groups of order 12,24,36, and 48 arent simple. i want discrete cases if possible not a generalization.
Use the classification of groups with six elements to show that A(4) has no subgroup with...
Use the classification of groups with six elements to show that A(4) has no subgroup with 6 elements. [ Hint: check that the product of any two elements of A(4) of order 2 has order 2]
show thar up to isomorphism there are two abelian groups of order 200that have exactly 7...
show thar up to isomorphism there are two abelian groups of order 200that have exactly 7 subgroups of order 2
Investigate the following theorems (h) For sets A, B and C we have i. A\(B ∪...
Investigate the following theorems (h) For sets A, B and C we have i. A\(B ∪ C) = (A\B) ∩ (A\C), ii. A\(B ∩ C) = (A\B) ∪ (A\C), iii. A ̸= B if and only if (A\B) ∪ (B\A) ̸= ∅, iv. A ∪ B ⊆ C if and only if A ⊆ C and B ⊆ C. What happens in the extreme case(s) where some (or all) sets are empty?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT