Unformatted text preview: psubgroups of G . (h) If G and H are ﬁnite groups of the same order, then, for every prime p , their Sylow psubgroups have the same order. (i) There is a group of order 400 having exactly 8 Sylow 5subgroups. [9 pts] 2. Give an example of a ﬁnite group G having 3 Sylow psubgroups (for some prime p ) P , Q and R such that P ∩ Q = { e } and P ∩ R 6 = { e } . [3 pts] 3. Prove that there are no simple groups of order 300, 312, 616 or 1000. [3 pts]...
View
Full Document
 Spring '11
 Johnson
 Algebra, Cyclic group, Simple group, Sylow psubgroup, Sylow theorems

Click to edit the document details