Question

What does "subgroup of $F_n$ consisting of all words of exponent sum $k$" mean?

score 38 · Answer 1 · 2026-03-25 12:49:39

38

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What does "subgroup of $F_n$ consisting of all words of exponent sum $k$" mean?

Published on 25 Mar 2026 - 12:49

score 280 · Answer 2 · 2026-03-26 03:00:33

280

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Free groups as free product of infinite cyclic groups

Published on 26 Mar 2026 - 3:00

score 51 · Answer 3 · 2026-03-27 10:17:04

51

Views

Generators of free groups are really generators

Published on 27 Mar 2026 - 10:17

score 104 · Answer 4 · 2026-03-26 23:09:48

104

Views

Factor group of a free group

Published on 26 Mar 2026 - 23:09

score 215 · Answer 5 · 2021-01-23 15:23:25

215

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Final object in the "free group" category $\mathscr{F}^A$

Published on 23 Jan 2021 - 15:23

score 104 · Answer 6 · 2021-01-26 23:40:45

104

Views

Elements of a free group commute if their powers commute

Published on 26 Jan 2021 - 23:40

score 43 · Answer 7 · 2026-03-26 19:20:10

43

Views

How to prove that the characteristic polynomial of this specific matrix is not the power of a linear polynomial?

Published on 26 Mar 2026 - 19:20

score 191 · Answer 8 · 2026-03-29 07:00:37

191

Views

S_3 is a quotient of the free group F({x,y})

Published on 29 Mar 2026 - 7:00

score 353 · Answer 9 · 2026-03-26 23:11:03

353

Views

How's the 'integer lattice' or the 'direct sum' of $\mathbb{Z} \oplus \mathbb{Z}$ not a Free group?

Published on 26 Mar 2026 - 23:11

score 115 · Answer 10 · 2021-02-03 07:42:41

115

Views

Is this relationship on subcartesian products of quotient groups over the free group correct?

Published on 03 Feb 2021 - 7:42

score 278 · Answer 11 · 2026-03-27 13:11:26

278

Views

Why the group $\langle x,y\mid x^3, y^3, yxyxy\rangle$ is not trivial?

Published on 27 Mar 2026 - 13:11

score 124 · Answer 12 · 2026-03-27 13:10:37

124

Views

For any primitive element $a$ in a free group of rank two we have $a^k ba^l=b$ only if $(k,l)=(0,0)$ provided $b\not\in \langle a\rangle$

Published on 27 Mar 2026 - 13:10

score 39 · Answer 13 · 2021-02-27 17:05:34

39

Views

Example of homomorphism $\underset{\alpha \in A}{\ast} \pi_1(U_\alpha) \to \pi_1(X)$, where $U_\alpha \ni x_0$ are an open cover of $(X,x_0)$.

Published on 27 Feb 2021 - 17:05

score 122 · Answer 14 · 2026-03-26 02:57:40

122

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Presentation of the amalgamated product of $G_1$ and $G_2$ above $H$ is $ \langle S_1,S_2\; ; \; R_1,R_2,\phi_1(s)\phi_{2}^{-1}(s),s \in S \rangle $

Published on 26 Mar 2026 - 2:57

score 53 · Answer 15 · 2021-03-09 16:21:50

53

Views

Slick argument to find free group in $SO(4)$

Published on 09 Mar 2021 - 16:21

List Question

What does "subgroup of $F_n$ consisting of all words of exponent sum $k$" mean?

Free groups as free product of infinite cyclic groups

Generators of free groups are really generators

Factor group of a free group

Final object in the "free group" category $\mathscr{F}^A$

Elements of a free group commute if their powers commute

How to prove that the characteristic polynomial of this specific matrix is not the power of a linear polynomial?

S_3 is a quotient of the free group F({x,y})

How's the 'integer lattice' or the 'direct sum' of $\mathbb{Z} \oplus \mathbb{Z}$ not a Free group?

Is this relationship on subcartesian products of quotient groups over the free group correct?

Why the group $\langle x,y\mid x^3, y^3, yxyxy\rangle$ is not trivial?

For any primitive element $a$ in a free group of rank two we have $a^k ba^l=b$ only if $(k,l)=(0,0)$ provided $b\not\in \langle a\rangle$

Example of homomorphism $\underset{\alpha \in A}{\ast} \pi_1(U_\alpha) \to \pi_1(X)$, where $U_\alpha \ni x_0$ are an open cover of $(X,x_0)$.

Presentation of the amalgamated product of $G_1$ and $G_2$ above $H$ is $ \langle S_1,S_2\; ; \; R_1,R_2,\phi_1(s)\phi_{2}^{-1}(s),s \in S \rangle $

Slick argument to find free group in $SO(4)$

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