Equation 677 Database

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Magma cbdef8cd5f51…

magma cbdef8cd5f51
Size
707
Isomorphism class hash
cbdef8cd5f51b12dbdb49731c95e1483c8c4fe86c5db62a23cd0124199cd83a1
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 10:46:48
Display reorder
302,300,301,303,304,305,656,57,58,54,55,56,59,263,262,261,259,258,260,79,78,80,82,83,81,248,247,246,250,249,251,275,274,273,272,270,271,267,269,268,264,266,265,136,135,137,134,132,133,277,278,276,279,280,281,99,101,100,97,98,96,145,144,146,149,147,148,534,533,535,531,530,532,384,383,385,380,381,382,521,520,522,523,554,591,569,568,570,571,572,573,438,443,439,440,441,442,538,536,539,540,541,537,548,398,587,399,547,586,526,594,527,528,529,557,506,505,507,502,503,504,515,514,516,511,512,513,633,629,610,606,609,611,634,627,639,632,684,673,675,677,703,685,704,686,672,657,6,7,9,10,11,8,244,243,245,242,241,240,142,141,143,139,140,138,176,175,174,177,178,179,210,212,211,213,214,215,228,229,230,232,231,233,16,15,17,14,12,13,41,40,39,38,36,37,237,239,238,234,236,235,252,253,254,257,255,256,339,338,334,335,336,337,465,464,462,463,551,590,588,549,550,589,400,401,447,446,448,449,444,445,459,458,460,461,456,457,559,560,596,580,576,561,579,597,508,509,510,552,387,386,388,389,390,391,372,371,373,368,369,370,350,355,351,352,353,354,655,653,641,617,649,645,631,626,640,630,679,680,681,661,702,663,701,687,671,664,84,85,87,88,89,86,91,90,92,95,93,94,157,156,158,160,161,159,206,205,204,207,208,209,184,183,185,181,182,180,150,152,151,154,155,153,64,63,65,62,60,61,29,28,27,26,24,25,21,23,22,19,20,18,69,71,70,67,68,66,362,367,363,364,365,366,345,344,346,347,543,583,592,555,556,593,524,525,454,453,455,450,451,452,498,497,499,500,501,496,558,575,599,581,577,574,578,598,517,518,519,553,481,480,482,483,478,479,484,489,485,486,487,488,494,493,495,490,491,492,654,650,647,623,642,648,622,625,638,621,676,674,666,669,699,670,700,688,667,668,4,5,0,2,1,3,126,128,127,130,131,129,168,170,169,171,172,173,198,199,200,203,201,202,227,226,225,224,222,223,165,167,166,163,164,162,31,30,32,35,33,34,196,195,197,193,194,192,216,217,218,221,219,220,74,73,72,75,76,77,325,324,326,327,322,323,331,330,332,333,328,329,321,320,318,319,542,595,566,565,567,562,563,564,356,361,357,358,359,360,376,375,377,378,379,374,546,349,584,348,545,585,340,582,341,342,343,544,475,474,476,477,472,473,467,466,468,469,470,471,652,651,643,618,644,646,620,624,637,619,683,678,682,658,697,660,698,662,665,659,191,189,188,186,187,190,123,125,124,121,122,120,50,49,48,53,51,52,111,113,112,109,110,108,107,106,105,104,102,103,282,283,284,287,285,286,118,117,119,116,114,115,44,43,42,47,45,46,297,299,298,294,296,295,291,293,292,288,290,289,425,424,420,421,422,423,413,412,408,409,410,411,407,406,402,403,404,405,309,308,310,311,307,306,435,434,436,437,432,433,600,601,602,603,604,605,415,414,416,417,418,419,316,315,317,312,313,314,430,429,431,426,427,428,395,394,396,397,392,393,636,635,613,607,612,615,614,616,628,608,692,694,691,695,706,693,705,689,690,696 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#fd7de578af0812c41995e8ffd4ad83dcb5427b7eb760f7a58401ca67989e247a, M = {30, 31, 32, 33, 34, 35, 135} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-07 10:46:50 · history