Equation 677 Database

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Magma 1bb28cfbbb4f…

magma 1bb28cfbbb4f
Size
707
Isomorphism class hash
1bb28cfbbb4f5a5a622eced5b9685e0fbea4cac3495a75c1abf0164dc7998025
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 00:30:32
Display reorder
555,554,556,559,557,558,638,257,256,252,253,254,255,197,194,198,193,196,195,2,1,3,4,5,0,152,151,153,148,149,150,104,103,105,106,101,102,31,30,32,33,34,35,27,26,28,29,24,25,175,174,170,171,172,173,22,21,23,18,19,20,262,261,263,258,259,260,310,309,311,306,307,308,478,477,479,475,476,474,589,588,590,586,587,591,446,445,447,450,448,449,529,528,530,525,526,527,333,335,334,338,336,337,535,534,536,531,532,533,540,452,451,454,455,453,560,562,561,564,563,592,593,595,594,598,596,597,632,643,633,610,611,606,622,644,647,698,669,678,697,679,696,699,688,703,706,705,156,155,157,225,158,154,79,82,80,81,78,223,115,114,116,117,118,113,162,161,163,226,159,160,179,178,180,227,176,177,74,73,75,76,77,72,56,55,57,58,59,54,272,271,273,274,275,270,245,244,240,241,242,243,234,239,235,236,237,238,132,131,133,134,135,224,362,361,363,365,366,364,421,423,422,424,425,426,411,410,409,412,413,414,570,569,568,565,567,566,419,418,420,415,416,417,444,443,442,440,441,439,493,492,494,495,496,497,462,464,463,467,465,466,399,398,397,401,402,400,631,627,629,630,649,650,625,642,626,682,681,695,683,659,674,673,667,684,694,701,287,286,282,283,284,285,38,41,39,40,37,36,97,96,98,99,100,95,279,278,280,281,276,277,143,142,144,145,146,147,94,93,89,90,91,92,212,211,213,214,215,216,87,86,88,83,84,85,11,10,6,7,8,9,44,43,45,46,47,42,290,289,291,292,293,288,521,520,519,518,516,517,381,380,379,384,382,383,511,510,512,515,513,514,390,389,388,386,387,385,500,499,498,502,503,501,605,604,603,601,602,600,458,457,456,460,461,459,509,508,507,505,506,504,542,541,543,544,545,546,607,646,618,645,612,617,624,623,619,692,675,690,686,657,665,677,658,693,676,700,16,15,17,12,13,14,219,231,220,221,233,222,218,217,230,232,228,229,303,302,304,305,301,300,53,52,48,49,50,51,313,312,314,315,316,317,298,297,299,294,295,296,269,268,264,265,266,267,136,141,137,138,139,140,250,249,251,246,247,248,210,209,205,206,207,208,392,391,393,395,396,394,406,408,407,403,404,405,428,427,429,432,430,431,433,435,434,438,436,437,350,351,552,354,352,353,550,549,551,547,548,553,539,538,537,331,330,332,482,481,480,484,485,483,489,491,490,488,486,487,615,616,614,609,608,613,621,651,648,702,666,685,704,663,668,680,664,689,691,687,190,189,191,192,187,188,164,167,165,166,169,168,199,204,200,201,202,203,183,182,184,185,186,181,326,328,327,324,325,329,65,64,60,61,62,63,107,112,108,109,110,111,323,322,319,318,320,321,129,128,130,125,126,127,124,123,119,120,121,122,71,70,66,67,68,69,347,349,348,344,345,346,341,340,339,343,342,599,571,573,572,575,576,574,359,358,360,355,356,357,581,580,582,583,584,585,577,579,578,522,523,524,376,378,377,375,373,374,369,368,367,371,372,370,472,471,473,468,469,470,641,628,639,640,635,634,620,636,637,671,656,662,670,653,652,655,654,660,661,672 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#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = {120, 121, 122, 123, 124, 125, 134} 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 00:30:33 · history