Equation 677 Database

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Magma 361a218d52d0…

magma 361a218d52d0
Size
381
Isomorphism class hash
361a218d52d0359d3d523d0f5f8e43acdbd410a37c6230a9e550fc117fda2aae
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:34:57
Display reorder
380,281,80,75,90,95,86,194,199,204,179,184,189,46,37,42,270,2,219,209,214,234,224,229,51,56,60,66,70,276,129,134,139,144,149,300,302,301,304,305,303,259,264,254,244,249,23,29,34,14,19,269,154,159,299,164,169,174,109,289,104,124,114,294,3,239,119,340,369,334,364,359,339,374,351,345,378,280,81,76,91,96,85,190,195,200,176,181,186,45,36,41,271,1,216,206,210,230,220,225,50,55,61,65,71,275,125,130,136,140,145,322,323,321,319,320,318,255,260,250,241,246,20,26,31,11,16,265,151,156,295,161,166,170,105,286,100,121,111,291,0,235,116,341,365,330,360,356,335,370,350,346,375,283,83,78,93,98,88,192,197,202,177,182,187,48,38,43,273,6,217,207,212,232,222,227,53,58,63,68,73,278,127,132,137,142,147,325,326,324,328,329,327,257,262,252,242,247,24,27,32,12,17,267,152,157,297,162,167,172,107,287,102,122,112,292,7,237,117,343,367,332,362,357,337,372,352,348,377,282,82,77,92,97,87,191,196,201,175,180,185,47,35,40,272,4,215,205,211,231,221,226,52,57,62,67,72,277,126,131,135,141,146,312,313,314,315,316,317,256,261,251,240,245,21,25,30,10,15,266,150,155,296,160,165,171,106,285,101,120,110,290,5,236,115,342,366,331,361,355,336,371,354,347,376,284,84,79,94,99,89,193,198,203,178,183,188,49,39,44,274,8,218,208,213,233,223,228,54,59,64,69,74,279,128,133,138,143,148,307,308,306,310,311,309,258,263,253,243,248,22,28,33,13,18,268,153,158,298,163,168,173,108,288,103,123,113,293,9,238,118,344,368,333,363,358,338,373,353,349,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {74} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:34:58 · history