Equation 677 Database

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Magma a85037d60d68…

magma a85037d60d68
Size
581
Isomorphism class hash
a85037d60d6800b722770c8a8ad83a6a9faabe57cc139ded250a70b83b9a34e1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 580) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 13:18:33
Display reorder
580,442,434,441,433,450,449,448,418,426,411,419,427,412,420,428,413,421,429,414,422,430,415,423,431,408,416,424,409,417,425,410,443,451,436,444,452,437,445,453,438,446,454,439,447,455,432,440,473,458,466,474,459,467,475,460,468,476,461,469,477,462,470,478,463,471,479,456,464,472,457,465,386,395,403,387,396,404,388,397,405,389,398,406,385,393,401,384,392,400,390,399,407,391,394,402,435,520,519,518,512,531,511,522,523,521,525,532,524,564,567,571,568,573,574,579,577,36,35,33,32,37,34,31,15,16,17,18,19,20,21,22,23,1,0,2,3,4,5,6,7,8,9,10,11,12,13,14,39,40,41,42,43,44,45,46,47,24,25,26,27,28,29,30,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,48,49,50,51,52,53,54,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,72,73,74,75,76,77,78,38,502,504,503,526,534,537,539,538,533,513,506,505,562,557,563,558,560,561,559,556,381,380,378,377,382,379,376,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,288,289,290,291,292,293,294,295,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,312,313,314,315,316,317,318,319,383,499,501,500,497,498,510,509,516,517,529,530,536,551,554,552,555,549,550,548,553,174,173,171,170,175,172,169,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,144,145,146,147,148,149,150,151,152,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,168,113,114,115,116,117,118,119,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,137,138,139,140,141,142,143,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,176,482,484,483,480,481,508,507,515,514,527,528,535,566,572,569,575,570,576,565,578,204,203,201,200,205,202,199,287,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,207,208,209,210,211,212,213,214,215,192,193,194,195,196,197,198,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,216,217,218,219,220,221,222,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,240,241,242,243,244,245,246,206,490,489,488,485,486,487,495,496,494,491,492,493,544,547,545,541,542,543,540,546 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 581 = 1 + 5*116, 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#bb54efccb01a6693da6fe7fa5911dfb34357e705bbecdb05a2adcd645e999db5, M = {116} 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, 116): MacNeish's product over GF(4) x GF(29); 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: 1.

last edited by qawbecrdtey at 2026-10-03 13:18:34 · history