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Index of $G^n$ in $G$, an $s$-step nilpotent group of rank $\leq r$

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#abstract-algebra #group-theory #nilpotent-groups
216
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Intersection of a nested sequence of subgroups

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#group-theory #nilpotent-groups
100
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Growth rate of free nilpotent group of rank $r$ and nilpotency index $s$.

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#abstract-algebra #group-theory #free-groups #nilpotent-groups #subgroup-growth
175
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Nilpotency class of Frattini subgroup and group order

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#abstract-algebra #group-theory #finite-groups #nilpotent-groups #frattini-subgroup
47
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On the nilpotency class of a certain subgroup

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#group-theory #nilpotent-groups
102
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Basic theorem for solvable groups not true for nilpotent groups - counterexample.

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#group-theory #examples-counterexamples #solvable-groups #quotient-group #nilpotent-groups
97
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A polynomial algorithm to determine whether a finite group is nilpotent

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#group-theory #finite-groups #algorithms #computational-complexity #nilpotent-groups
46
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Reduce completion time of projects with constraints

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#nilpotent-groups
96
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Are Triangle Groups virtually nilpotent?

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#group-theory #geometric-group-theory #nilpotent-groups
68
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Question regarding writing a group of order $p^2qr$ using notations

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#abstract-algebra #group-theory #finite-groups #semidirect-product #nilpotent-groups
358
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Let $G$ be a nilpotent group generated by a finite set of torsion (i.e. finite order) elements. Show that $G$ is finite.

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#abstract-algebra #group-theory #finite-groups #nilpotent-groups
89
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Proving that a quotient is virtually a nilpotent group

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#group-theory #nilpotent-groups
185
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Commutator power lying in commutator subgroup

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#group-theory #torsion-groups #nilpotent-groups
282
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Are all nilpotent groups hamiltonian?

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#abstract-algebra #group-theory #finite-groups #nilpotent-groups
1.8k
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Commutator subgroup of Heisenberg group.

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#abstract-algebra #group-theory #quotient-group #nilpotent-groups #heisenberg-group

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