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Results tagged with group-cohomology
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user 23827
In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.
1
vote
A finite group that splits and does not split
I take it Pablo your question can be rephrased as follows. Does there exist an epimorphism $\tau\colon A\ltimes C\to A$ where $A$ acts irreducibly on $C$ and where $\ker(\tau)\ne C$? If this is your q …
- 1,991
4
votes
Accepted
When is an almost simple group a split extension of its socle?
See the following paper:
A. Lucchini, F. Menegazzo, M. Morigi.
On the existence of a complement for a finite simple group in its automorphism group. Special issue in honor of Reinhold Baer (1902–1979) …
- 1,991
0
votes
The sum of the carries when adding and multiplying two numbers in base p
I was asked (offline) for a proof of the formula for the sum of the carries $\pi_p(a,b)$ when multiplying $a$ and $b$ in base $p$.
Proof. Multiplying the base-$p$ expansions $a=\sum_{k\ge0}a_kp^k$ an …
- 1,991
12
votes
2
answers
760
views
The sum of the carries when adding and multiplying two numbers in base p
Let $\sigma_p(m,n)$ (resp. $\pi_p(m,n)$) denote the sum of the carries when adding
(resp. multiplying) the numbers $m=\sum_{k\ge0}m_kp^k$ and $n=\sum_{k\ge0}n_kp^k$ using base-$p$ arithmetic where $m_ …
- 1,991