Skip to main content
MathOverflow

Return to Answer

Fixed the strange-looking citation.
Source Link
edit approved Feb 24, 2021 at 1:19
Carl-Fredrik Nyberg Brodda
edit approved Feb 24, 2021 at 1:19
Carl-Fredrik Nyberg Brodda
  • 6.5k
  • 4
  • 27
  • 62

Reference:

Higman, Graham

A finitely generated infinite simple groupHigman, Graham, A finitely generated infinite simple group, J. J Lond. London Math. Soc. 26, 61-64 (1951). 61--64ZBL0042.02201.

It is shown that G$G$ is infiniteinfinite and has no proper normal subgroups of of finite index, except G$G$.

It is easy to see that this group is perfect: itit has trivial abelianization.

I have heard through the grapevine that the space $X$ with four one-cells and four two-cells (corresponding, respectively, to generators and relations) is the classifying space of the group (I don't have a reference).

Reference:

Higman, Graham

A finitely generated infinite simple group. J. London Math. Soc. 26, (1951). 61--64

It is shown that G is infinite and has no proper normal subgroups of finite index, except G.

It is easy to see that this group is perfect: it has trivial abelianization.

I have heard through the grapevine that the space $X$ with four one-cells and four two-cells (corresponding, respectively, to generators and relations) is the classifying space of the group (I don't have a reference).

Reference:

Higman, Graham, A finitely generated infinite simple group, J. Lond. Math. Soc. 26, 61-64 (1951). ZBL0042.02201.

It is shown that $G$ is infinite and has no proper normal subgroups of finite index, except $G$.

It is easy to see that this group is perfect: it has trivial abelianization.

I have heard through the grapevine that the space $X$ with four one-cells and four two-cells (corresponding, respectively, to generators and relations) is the classifying space of the group (I don't have a reference).

Source Link
Jeff Strom
Jeff Strom
  • 12.5k
  • 3
  • 48
  • 76

Reference:

Higman, Graham

A finitely generated infinite simple group. J. London Math. Soc. 26, (1951). 61--64

It is shown that G is infinite and has no proper normal subgroups of finite index, except G.

It is easy to see that this group is perfect: it has trivial abelianization.

I have heard through the grapevine that the space $X$ with four one-cells and four two-cells (corresponding, respectively, to generators and relations) is the classifying space of the group (I don't have a reference).