## Analog to the Chinese Remainder Theorem in groups other than Z_n.

The Chinese Remainder theorem is usually thought of as an isomorphism of rings, not just of cyclic groups. In this …

The Chinese Remainder theorem is usually thought of as an isomorphism of rings, not just of cyclic groups. In this …

(1) is certainly false in general, but some things like it hold at least formally. See e.g. “Motivation” in Knapp …

Let $W = mathbb C^n$, with the obvious representation of $S_n$. Lemma Let $lambda$ be a partition of $n$. The …

Malcev’s example is orderable. See https://doi.org/10.2307/2036896. So the answer is known and in the negative. There is a prominent example …

There is a theoretical answer (as opposed to an algorithmic answer) found in Björner and Brenti’s “Combinatorics of Coxeter groups”, …

Let $A$ be the additive group of bounded sequences of elements of $mathbb{Z}[sqrt{2}]$. Clearly $Acong Aoplusmathbb{Z}[sqrt{2}]cong Aoplusmathbb{Z}^2$ as abelian groups, …

Take the graph product $G = P times mathbb{Z}$ of the Petersen graph with the infinite path graph. This is …

The answer is no. Counterexamples include the Weyl groups of types E6, E7, and E8. For a proof that the …

I presume by “acyclic” you are referring to homology with $mathbb{Z}$ coefficients. There are many such examples. For instance, you …

I can answer Questions 1 and 4. Make sure you look at S. Carnahan’s answer. It deals with Questions 2 …