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The simple N-groups were classified by Thompson (1968, 1970, 1971, 1973, 1974, 1974b) in a series of 6 papers totaling about 400 pages.The simple N-groups consist of the special linear groups PSL 2 (q), PSL 3 (3), the Suzuki groups Sz(2 2n+1), the unitary group U 3 (3), the alternating group A 7, the Mathieu group M 11, and the Tits group.
Projective symplectic group, PSp 2n (q), PSp n (q) (not recommended), S 2n (q), Abelian group (archaic). O 2n + (q), PΩ 2n + (q). "Hypoabelian group" is an archaic name for this group in characteristic 2. Isomorphisms A 1 (2) is isomorphic to the symmetric group on 3 points of order 6. A 1 (3) is isomorphic to the alternating group A 4 (solvable).
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Dih n: the dihedral group of order 2n (often the notation D n or D 2n is used) K 4: the Klein four-group of order 4, same as Z 2 × Z 2 and Dih 2; D 2n: the dihedral group of order 2n, the same as Dih n (notation used in section List of small non-abelian groups) S n: the symmetric group of degree n, containing the n! permutations of n elements ...
General linear group, denoted by GL(n, F), is the group of n-by-n invertible matrices, where the elements of the matrices are taken from a field F such as the real numbers or the complex numbers. Group representation (not to be confused with the presentation of a group). A group representation is a homomorphism from a group to a general linear ...
The multiplicative group of upper unitriangular n × n matrices over any field F is a nilpotent group of nilpotency class n − 1. In particular, taking n = 3 yields the Heisenberg group H, an example of a non-abelian [6] infinite nilpotent group. [7] It has nilpotency class 2 with central series 1, Z(H), H.
Web-based tool to interactively compute group tables by John Jones; OEIS sequence A033948 (Numbers that have a primitive root (the multiplicative group modulo n is cyclic)) Numbers n such that the multiplicative group modulo n is the direct product of k cyclic groups: k = 2 OEIS sequence A272592 (2 cyclic groups)
N-group (finite group theory), a finite group all of whose local subgroups are solvable. Topics referred to by the same term This disambiguation page lists mathematics articles associated with the same title.