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# Questions tagged [computational-group-theory]

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### Is there any good methods for writing down basis for laws of groups?

I am wondering if there is a good method to write down a finite equational basis for a finite group. Especially I am wondering if there is a good method in following situations: We can write a group ...
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### Positivity of the alternating sum of indices for boolean interval of finite groups

Let $G$ be a finite group and $H$ a subgroup such that the interval $[H,G]$ is a boolean lattice. Let $L_1, \dots , L_n$ be the maximal subgroups of $G$ containing $H$. Let the alternative sum ...
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### About $c(A)$ in $c(A)|A|\leq |A^{-1}A|$

Let $G$ be a finite group, $\emptyset\neq A\subseteq G$, $A^{-1}:=\{ a^{-1}:a\in A\}$, and put $$c(A):=\max\{t\in \mathbb{Z}: t|A|\leq |A^{-1}A|\}$$ It is clear that $1\leq c(A)\leq \frac{|G|}{|A|}$, ...
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### programming to compute kernel quotient image of a $\mathbb{Z}$-module endomorphism

Let the integers $n\geq 2$, $k\geq 1$, $v=0$ or $1$ and $n_1,\cdots,n_k\geq 1$ such that $$\sum_{i=1}^k n_i+v=n.$$ Define $P_a^b=0$ if both $a,b$ are odd and $P_a^b={{[a/2]}\choose {[(a+b)/2]}}$ ...