MathOverflow

Consider the generalized Moore spectra $M(1) = \mathbb{S}/(2)$ and $M(1,4) = \mathbb{S}/(2,v_1^4)$, everything at the prime $p=2$. In [1] the authors construct a $v_2^{32}$-self map on $M(1,4)$. Their starting point is the fact that any map $M(1) \to...

My queastion is as follows:
Is there a locally finite perfect minimal non ($IG$)-$p$-group $G$ for a fixed prime p, i.e. every proper subgroup of $G$ is $IG$ but the group itself is not.
Recall that a group $K$ is IG (Invariably Generated) if $K\neq \bigcup_{g\in G}H^g$ for every proper subgroup $H$ of $K$-there are some other equivalent conditions- See for example ``Transitive groups with fixed-point free permutations" by J. Wiegold...

Let $k$ be a positive integer. Let $n$ and $m$ be positive integers with $m$ roughly $\log_2 n$, let $V$ be an $n$-dimensional vector space over $\mathbb{F}_2$, let $W$ be an $m$-dimensional vector space over $\mathbb{F}_2$, where $\mathbb{F}_2$ is the...

Let $N \subset M$ be a finite index inclusion of II$_1$ factors, and let $H(M|N)$ denote the Connes-St{\o}rmer relative entropy with respect to the trace. It is known that$$H(M|N) \leq \log [M:N],$$with equality if and only if the inclusion is extremal...