Best books

Archives

2-groups with an odd-order automorphism that is the identity by Mazurov V.D.

By Mazurov V.D.

Show description

Read Online or Download 2-groups with an odd-order automorphism that is the identity on involutions PDF

Similar symmetry and group books

Rotations, quaternions, and double groups

This precise monograph treats finite element teams as subgroups of the whole rotation team, delivering geometrical and topological tools which permit a distinct definition of the quaternion parameters for all operations. a huge characteristic is an uncomplicated yet complete dialogue of projective representations and their software to the spinor representations, which yield nice merits in precision and accuracy over the extra classical double workforce strategy.

The theory of groups

Maybe the 1st really recognized publication committed basically to finite teams was once Burnside's e-book. From the time of its moment variation in 1911 until eventually the looks of Hall's e-book, there have been few books of comparable stature. Hall's publication remains to be thought of to be a vintage resource for primary effects at the illustration conception for finite teams, the Burnside challenge, extensions and cohomology of teams, $p$-groups and masses extra.

Additional info for 2-groups with an odd-order automorphism that is the identity on involutions

Sample text

1. 31 Our general notation mainly concerns group theory — our standard reference being [28] — and homological algebra — our standard reference being [18]. In particular, if G is a finite group, recall that Op (G) , Op (G) , Op (G) and Op (G) respectively denote the minimal or the maximal normal subgroups of G with their index or their order being a power of p or prime ˆ except to p ; note that this notation still makes sense for a finite k ∗ -group G ˆ that Op (G) remains a p-group. For any pair of subgroups H and K of G , we denote by TG (K, H) the set of x ∈ G fulfilling xKx−1 ⊂ H .

But, as a matter of fact, when dealing with contravariant functors a from F to Ab (cf.

3), they coincide (cf. 4). 7 F(b,G) is a Frobenius P -category. 1; thus, since p does not divide |NG (P, e)/P ·CG (P )| (cf. 1. Let Q be a subgroup of P , K a subgroup of Aut(Q) containing FQ (Q) and ϕ : Q → P an F(b,G) -morphism such that ϕ(Q) is fully ϕK-normalized in F(b,G) ; in particular, denoting by f the block of CG (Q) such that (P, e) contains (Q, f ) , there is x ∈ G fulfilling (cf. 2. As above, denote by g the block of CG NPK (Q) such that (P, e) contains the Brauer (b, G)-pair (NPK (Q), g) .

Download PDF sample

Rated 4.70 of 5 – based on 17 votes

Comments are closed.