# Tagged Questions

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### Union of conjugates of a subgroup

Let $G$ be a finite group, $H \leq G$ a proper subgroup. It is well known that the union of the conjugates of $H$ does not cover $G$. I would like to know of more precise results (even in special ...
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### A question on direct limits of finite $p$-groups

Where can we find a well developed material on direct limits of finite $p$-groups? For instance, is there a characterization of such groups, which have a finite rank (that is every subgroup can be ...
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### A characterization of almost relatively free, finite $p$-groups

Let $G$ be a finite minimally $d$-generated $p$-group. If $G$ is relatively free, that is $G$ is a quotient of the free group $F$ on $d$ generators by a fully invariant subgroup of $F$, then the ...
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### A question on $p$-central $p$-groups

Let $p$ be a fixed prime. A group $G$ is termed $p$-central if every element of order $p$ in $G$ lies in the center. Having a finite $p$-group $G$ of rank $k$ (the least integer, such that every ...
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### Number of Normal subgroups In a p-Group

Dear all, Does someone know of any paper/method that enables us counting/estimating the number of normal subgroups of some p-group of order $p ^n$ ($n$ is some natural number ? ) . Is there anyway ...
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### Hall algebra for non-abelian p-groups ?

According to WP article on Hall algebras one counts the number of abelian subgroups in abelian group with fixed type of subgroup, group, quotient. Two things are claimed: 1) These numbers are ...
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### Center of p-groups

Can one show that any abelian $p$-group (not necessarily finite) is the center of a $p$-group and of index $p$?
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### Representation theory of p-groups in particular upper tringular matrices over F_p

Finite p-groups - have p^n elements by definition. According to WP there is rich structure theory. Question: How far is representation theory of p-groups is understood? In case this question is too ...
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### Maximal subgroups of a certain finite 2-group

The following came up in a problem on reconstruction of digraphs. I determined enough about the answer to satisfy the application completely, but still I am curious to know what the complete solution ...