Lee’s Reviews > Linear Representations of Finite Groups > Status Update

Serre's treatment of solvable, supersolvable, and nilpotent groups is perhaps the worst I have ever seen. For example, Theorem 14 states "Every p-group is nilpotent" and his proof is the following: "In view of the preceding it suffices to show that the center of every nontrivial p-group G is nontrivial. This is a consequence of the following lemma: ..."

"The preceding" is not as sufficient as he claims.

In the section paragraph of section 7.3, Serre writes:

"First choose a set of representatives S for the (H, K) double cosets of G; this means that G is the disjoint union of the KsH for s \in S (we could also write s \in K\G/H)."

The first part of this sentence should read:

"First choose a set of representatives S for the (K, H) double cosets of G;"

In the section paragraph of section 7.3, Serre writes:

"First choose a set of representatives S for the (H, K) double cosets of G; this means that G is the disjoint union of the KsH for s \in S (we could also write s \in K\G/H)."

The first part of this sentence should read:

"First choose a set of representatives S for the (K, S) double cosets of G;"

The exercises for section 5.9 are mis-numbered. An exercise 5.4 occurs in section 5.7, but the exercises in section 5.9 are numbered 5.4 and 5.5. They should be numbered 5.5 and 5.6, respectively.

There is a significant typo in the last set of equations on page 29: "f" should be present in each equality.