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answered Is there an easy way to tell if all eigenvalues of a unitary or self-adjoint matrix only have eigenvalues of multiplicity two?
Aug
16
revised Asymptotic density of finite abelian and solvable groups
Amended first sentence
Aug
16
comment Asymptotic density of finite abelian and solvable groups
OK, thanks, I've reworded my post.
Aug
16
answered Asymptotic density of finite abelian and solvable groups
Aug
15
comment Special linear groups contained in symplectic groups
Try the book by Kleidman, or papers of Kleidman and Liebeck
Aug
14
comment Reverse to Chinese Remainder Theorem
I'm not sure what you can expect here, beyond the trivial $|x^{\ast}| \leq \frac{m}{2}.$
Aug
14
comment When is a cubic polynomial a cube?
@Pietro: I thinks he means the (textspeak) shorthand for "laughing out loud", it's not a Mathematical symbol!
Aug
11
comment A question on conjugacy classes of central involutions in a finite group
In fact, the number of classes of central involutions is the number of $N_{G}(S)$ orbits by conjugation on $\Omega_{1}(Z(S)) \backslash \{1_{G}\},$ where $S$ is a Sylow $2$-subgroup and $\Omega_{1}(Z(S))$ is the subgroup of $Z(S)$ generated by its involutions.
Aug
9
comment Successive Schur covers
For a perfect group, it stops after (at most) one step. In general, I think the sequence can go on indefinitely ( eg, you can take $G_{0}$ to be be a Klein $$-group, and $G_{j}$ to be a dihedral $2$-group of order $2^{j+2}$ for each $j.$
Aug
6
comment A question on conjugacy classes of central involutions in a finite group
I don't know if you really said what you mean, but if there is a unique conjugacy class of involutions in $G$, the statement is true. By the way, I think you need to specify that $a$ and $b$ are distinct involutions.
Aug
4
comment If $~(c - b) ^ 2 + 3cb = a^3~$ has nonzero integer solutions, then $~(a,c) \gt 1~$ or $~(b,c) \gt 1$?
If $n$ is nice, it has at least one such factorization with $c$ and $b$ coprime, (which is all you need for the answer) but if $n$ is not squarefree, then there are such (rational integer) factorizations with $c$ and $b$ not coprime (eg $7^{3} = 14^{2}+ (7 \times 14) +7^{2}).$
Aug
2
comment Existence a finite capable p-group of class two
Is a capable group the same as a powerful group?
Jul
27
revised Isolated elements of primary order ($Z^*$-theorem revisited)
typos
Jul
27
comment quasiprimitive non-solvable groups
There are two cases to consider: $F^{*}(G)$ of order prime to $p,$ and $F^{*}(G)$ of order divisible by $p.$ In the second case you may further ask what happens whether $F(G)$ has order divisible by $p.$ If it does, the situation should be under control. If it doesn't, then I think that some component (quasisimple subnormal subgroup) will fail to have a regular orbit, and that is quite rare. I am not sure what happens if $F^{*}(G)$ has order prime to $p,$ though in that case, the group is not far from $p$-solvable.
Jul
26
comment quasiprimitive non-solvable groups
Earlier comment deleted:I had not noticed the characteristic restriction.
Jul
26
revised quasiprimitive non-solvable groups
typo
Jul
26
answered quasiprimitive non-solvable groups
Jul
25
comment Compute an arbitrary decimal place of $\pi$
You might look up to look up the Bailey-Borwein-Plouffe results about the hexadecimal representation of $\pi.$
Jul
25
comment quasiprimitive non-solvable groups
Your question needs to be more specific, I think. You need to tell us more precisely what you want/need to know