Chain Markov
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A comprehensive list of random walk inequalities?
26 votes

There I will list the inequalities and asymptotic theorems on random walks, that are currently known to me: Notation that will be used in the list: $\{X_n\}_{n = 1}^\infty$ are i.i.d. random variables....

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Finite groups in which all proper subgroups are cyclic
16 votes

All subgroups of a cyclic group (including the proper ones) are cyclic. And there is the following classification of non-cyclic finite groups, such that all their proper subgroups are cyclic: A ...

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Nonequivalent definitions in Mathematics
7 votes

One of the most classical examples is the word «algebra», which denotes not only a branch of mathematics, but also the following mathematical objects: In linear algebra an algebra is a vector space, ...

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Examples of common false beliefs in mathematics
7 votes

Uncorrelatedness implies independence This statement is indeed false. Suppose $X \sim U[-1, 1]$. Then $Cov(X, X^2) = EX^3 - EXEX^2 = 0$, but $X$ and $X^2$ are clearly not independent. However, that ...

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Examples of common false beliefs in mathematics
3 votes

The derived subgroup of a finite group equals to the set of all its commutators or equivalently A product of two commutators in a finite group is always a commutator This mistake is very ...

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Normal subgroup of Fitting length i contained in i-th term of upper Fitting series?
Accepted answer
1 votes

You have already done the case, when $i = 1$. Now suppose it i true for $i$. Let's prove it for $i+1$. Suppose $H \triangleleft G$ has Fitting length $i+1$. That means $\frac{H}{U_iH}$ is nilpotent. ...

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