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Janko group J2

Index Janko group J2

In the area of modern algebra known as group theory, the Janko group J2 or the Hall-Janko group HJ is a sporadic simple group of order. [1]

25 relations: Academic Press, Characteristic (algebra), Conway group, Conway group Co1, Covering groups of the alternating and symmetric groups, Group of Lie type, Group theory, Hall–Janko graph, Hurwitz's automorphisms theorem, Index of a subgroup, Janko group J3, Journal of Algebra, Leonard Eugene Dickson, Modular representation theory, Monster group, Near polygon, Order (group theory), Outer automorphism group, Rank 3 permutation group, Robert Griess, Schur multiplier, Sporadic group, Subquotient, Zvonimir Janko, (2,3,7) triangle group.

Academic Press

Academic Press is an academic book publisher.

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Characteristic (algebra)

In mathematics, the characteristic of a ring R, often denoted char(R), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0) if the sum does indeed eventually attain 0.

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Conway group

In the area of modern algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced by.

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Conway group Co1

In the area of modern algebra known as group theory, the Conway group Co1 is a sporadic simple group of order.

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Covering groups of the alternating and symmetric groups

In the mathematical area of group theory, the covering groups of the alternating and symmetric groups are groups that are used to understand the projective representations of the alternating and symmetric groups.

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Group of Lie type

In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Hall–Janko graph

In the mathematical field of graph theory, the Hall–Janko graph, also known as the Hall-Janko-Wales graph, is a 36-regular undirected graph with 100 vertices and 1800 edges.

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Hurwitz's automorphisms theorem

In mathematics, Hurwitz's automorphisms theorem bounds the order of the group of automorphisms, via orientation-preserving conformal mappings, of a compact Riemann surface of genus g > 1, stating that the number of such automorphisms cannot exceed 84(g − 1).

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Index of a subgroup

In mathematics, specifically group theory, the index of a subgroup H in a group G is the "relative size" of H in G: equivalently, the number of "copies" (cosets) of H that fill up G. For example, if H has index 2 in G, then intuitively half of the elements of G lie in H. The index of H in G is usually denoted |G: H| or or (G:H).

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Janko group J3

In the area of modern algebra known as group theory, the Janko group J3 or the Higman-Janko-McKay group HJM is a sporadic simple group of order.

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Journal of Algebra

Journal of Algebra (ISSN 0021-8693) is an international mathematical research journal in algebra.

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Leonard Eugene Dickson

Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician.

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Modular representation theory

Modular representation theory is a branch of mathematics, and that part of representation theory that studies linear representations of finite groups over a field K of positive characteristic.

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Monster group

In the area of modern algebra known as group theory, the Monster group M (also known as the Fischer–Griess Monster, or the Friendly Giant) is the largest sporadic simple group, having order The finite simple groups have been completely classified.

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Near polygon

In mathematics, a near polygon is an incidence geometry introduced by Ernest E. Shult and Arthur Yanushka in 1980.

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Order (group theory)

In group theory, a branch of mathematics, the term order is used in two unrelated senses.

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Outer automorphism group

In mathematics, the outer automorphism group of a group,, is the quotient,, where is the automorphism group of and) is the subgroup consisting of inner automorphisms.

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Rank 3 permutation group

In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits.

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Robert Griess

Robert Louis Griess, Jr. (born 1945, Savannah, Georgia) is a mathematician working on finite simple groups and vertex algebras.

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Schur multiplier

In mathematical group theory, the Schur multiplier or Schur multiplicator is the second homology group H2(G, Z) of a group G. It was introduced by in his work on projective representations.

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Sporadic group

In group theory, a discipline within mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups.

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Subquotient

In the mathematical fields of category theory and abstract algebra, a subquotient is a quotient object of a subobject.

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Zvonimir Janko

Zvonimir Janko (born 26 November 1932) is a Croatian mathematician who is the eponym of the Janko groups, sporadic simple groups in group theory.

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(2,3,7) triangle group

In the theory of Riemann surfaces and hyperbolic geometry, the triangle group (2,3,7) is particularly important.

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Redirects here:

Hall-Janko group, Hall-Janko-Wales group, Hall–Janko group.

References

[1] https://en.wikipedia.org/wiki/Janko_group_J2

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