All Questions
7
questions
18
votes
1
answer
6k
views
What is the number of Sylow p subgroups in $S_p$?
I am reading the Wikipedia article entitiled Sylow theorems. This short segment of the article reads:
Part of Wilson's theorem states that
$(p-1)!$ is congruent to $-1$ (mod $p$) for every prime $p$....
- 3,711
3
votes
2
answers
953
views
Permutations minus Transpositions
I want a formula that allows me to find all the permutations in $S_n$ (which is the set of all the integers from 1 to $n$) which don't contain a transposition.
Attempt:
Lets call $g(n)$ the ...
- 857
3
votes
0
answers
82
views
'Randomness' of inverses of $(\mathbb{Z}/p \mathbb{Z})^\times$
Suppose you are given the group $(\mathbb{Z} / p \mathbb{Z})^{\times}$, where $p$ is prime. Let $A_p$ denote the sequence whose $j$th element is the inverse of $[j]$. For instance, if $p = 7$, the ...
- 47
3
votes
1
answer
283
views
Symmetry in the set of integers that cannot be written as $ap+bq$ where $a,b$ are non-negative integers for relatively prime $p,q$
I was studying symmetries (as an introduction to Group Theory) and found this question-
Let $p,q$ be relatively prime positive integers and let $X$ be the set of integers that cannot be written as $...
- 9,592
2
votes
1
answer
211
views
Select k no.s from 1 to N with replacement to have a set with at least one co-prime pair
Given $1$ to $N$ numbers. You have to make array of $k$ no.s using those no.s, where repetition of same no. is also allowed, such that at least one pair in that chosen array is co-prime. Find no. of ...
- 269
0
votes
0
answers
145
views
Given a finite group, does this equation involving group's order, a partition of it and centralizers' orders hold?_Attempt#2
After failing this attempt, I've revised my proof sketch and I've come to the following version of the equation in the title.
So, let $G$ be a finite group, say $G=\lbrace e,a_1,\dots,a_{n-1} \rbrace$...
user615081
0
votes
1
answer
430
views
Find the count of unique subset sums in a powerset
Given a list of integers, I want to find the count of unique sums for all possible subsets of length $N$.
I don't want to know the sum, or the subsets, just the count of possible unique sums for ...
- 149