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8h
comment Computing a transversal of a subgroup $H$ of $G$ in expected $O(|G : H|^2 \log |G : H| + |H|)$ time
It may be that this question will come to Derek Holt's notice in due course. He should have more insight than most into the issues you raise.
2d
revised real representation of a product group
typo
2d
revised real representation of a product group
added "associative"
May
26
comment Finite groups whose non-trivial elements have no fixed points
Probably better on Mathstackexchange.
May
24
comment Localized at $p$ integral representations of finite elementary $p$-groups
That is the cyclic case. I the non-cyclic elementary Abelia case, (which you have to look further back for, working from the references in Jones' paper), there are infinitely many isomorphism classes when $ n >1.$
May
23
revised A simple group that its order divide order of an alternating group
explained original question changed.
May
23
revised For $k>3$ does there exist an odd prime $q_k$ such that $p_k=2^kq_k+1$ is prime and $p_k$ divides $a_k=\dfrac{3^{2^{k-1}}+1}{2}$?
typo
May
23
revised A simple group that its order divide order of an alternating group
typo
May
23
answered A simple group that its order divide order of an alternating group
May
23
comment Localized at $p$ integral representations of finite elementary $p$-groups
There are infinitely many isomorphism types for $n >1.$ The number of isomorphism types is actually at least $1 + 2h_{p}$ when $n =1$, where $h_{p}$ is the class number of $\mathbb{Z}[\omega]$ and $\omega$ is a primitive $p$-th root of unity. For references, see for example projecteuclid.org/euclid.mmj/1028998908.
May
22
comment For natural numbers 1 to n, is the square of their sum equal to the sum of their cubes?
This probably belongs on Mathstackexchange. For any positive integer $k$, the sums $\sum_{j=1}^{n}j^{k}$ are well-studied and reasonably well understood. In particular, it is well-know and easy to prove by induction that $\sum_{j=1}^{n}j = \frac{n(n+1)}{2}$ and $\sum_{j=1}^{n} j^{3} = \left(\frac{n(n+1)}{2}\right)^{2}.$ This explains your observations and verifies that the answer is positive for all $n$.
May
22
revised For $k>3$ does there exist an odd prime $q_k$ such that $p_k=2^kq_k+1$ is prime and $p_k$ divides $a_k=\dfrac{3^{2^{k-1}}+1}{2}$?
expanded explanatio
May
22
revised real representation of a product group
added extra sentence of explanation
May
22
revised real representation of a product group
added alternative viewpoint
May
22
answered For $k>3$ does there exist an odd prime $q_k$ such that $p_k=2^kq_k+1$ is prime and $p_k$ divides $a_k=\dfrac{3^{2^{k-1}}+1}{2}$?
May
22
revised real representation of a product group
typo-spacing issue
May
20
revised real representation of a product group
expanded
May
19
comment A Diophantine equation with prime powers
In the Pell like case, how do you decide whether $x$ is prime or not, and if so, whether $y$ is also prime?
May
19
revised real representation of a product group
gave more explanation
May
19
awarded  Enlightened