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The sporadic group HJ, also denoted J_2.

A finite group L is quasisimple if L=[L,L] and L/Z(L) is a simple group.

A property of finite simple groups which is known for all such groups.

There are many unsolved problems in mathematics. Several famous problems which have recently been solved include: 1. The Pólya conjecture (disproven by Haselgrove 1958, ...

The image of A_5×A_5 in the special orthogonal group SO(4), where A_5 is the icosahedral group.

Every finite group of order n can be represented as a permutation group on n letters, as first proved by Cayley in 1878 (Rotman 1995).

The cubic groups are the point groups T_h and O_h together with their pure rotation subgroups T_d, T, and O (Cotton 1990, pp. 433-434).

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

The general unitary group GU_n(q) is the subgroup of all elements of the general linear group GL(q^2) that fix a given nonsingular Hermitian form. This is equivalent, in the ...

In the plane, there are 17 lattice groups, eight of which are pure translation. In R^3, there are 32 point groups and 230 space groups. In R^4, there are 4783 space lattice ...