Equation 677 Database

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Magma 297cdc44a116…

magma 297cdc44a116
Size
707
Isomorphism class hash
297cdc44a1160d193ae496f52329c09945e944b49d843db0cf28ffa3ad5d281e
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
2026-10-08 05:52:15
Display reorder
539,538,540,536,537,535,615,162,167,163,164,165,166,206,207,208,209,204,205,13,12,14,15,16,17,218,217,219,220,221,216,213,212,214,215,210,211,23,22,18,19,20,21,136,135,137,132,133,134,229,228,230,231,232,233,4,3,5,1,0,2,64,63,65,60,61,62,304,303,305,301,300,302,470,472,471,473,474,475,561,560,562,563,564,565,584,583,585,581,582,580,371,370,369,367,368,366,377,376,375,374,372,373,415,414,416,413,411,412,408,410,409,573,598,574,549,548,547,550,551,552,596,595,597,592,593,594,616,639,643,640,611,606,635,645,647,699,671,682,696,683,698,700,686,703,706,705,67,66,68,69,70,71,130,131,126,127,128,129,148,147,149,144,145,146,157,156,158,159,160,161,117,116,118,119,114,115,289,288,290,291,292,293,234,239,235,236,237,238,278,277,279,280,281,276,275,274,270,271,272,273,48,53,49,50,51,52,58,57,59,54,55,56,350,349,348,353,351,352,527,526,525,523,524,522,491,493,492,490,488,489,357,359,358,356,354,355,361,360,362,364,365,363,521,520,519,516,517,518,499,498,497,495,496,494,331,332,330,334,335,333,544,546,545,543,541,542,609,607,631,610,648,649,626,642,627,681,680,693,684,661,674,665,667,676,687,697,251,250,246,247,248,249,41,36,37,38,39,40,93,92,94,95,90,91,240,245,241,242,243,244,25,24,26,27,28,29,44,43,45,46,47,42,190,189,191,186,187,188,110,109,111,112,113,108,123,122,124,125,120,121,269,268,264,265,266,267,227,226,222,223,224,225,513,515,514,572,511,512,391,575,392,395,393,394,507,506,508,509,510,528,465,464,466,467,468,469,402,404,403,405,406,407,605,604,603,600,601,602,379,378,380,381,382,383,555,554,556,559,557,558,570,569,571,566,567,568,625,646,620,644,618,612,619,608,621,694,677,691,688,664,666,679,659,692,675,701,170,169,171,172,173,168,89,84,85,86,87,88,75,74,76,77,72,73,309,308,310,311,306,307,195,194,196,197,192,193,313,312,314,315,316,317,298,297,299,294,295,296,98,97,99,100,101,96,105,104,106,107,102,103,284,283,285,286,287,282,83,82,78,79,80,81,400,399,401,397,398,396,480,479,481,476,477,478,344,343,342,346,347,345,385,384,386,387,388,389,482,484,483,485,486,487,444,446,445,442,443,441,503,505,504,502,500,501,339,341,340,337,338,336,436,435,437,438,439,440,628,629,632,633,630,614,617,651,650,702,670,685,704,658,668,678,657,689,695,690,261,260,262,263,258,259,185,180,181,182,183,184,198,203,199,200,201,202,256,255,257,252,253,254,326,328,327,324,325,329,177,176,178,179,174,175,7,6,8,9,10,11,322,321,323,319,318,320,31,30,32,33,34,35,139,138,140,141,142,143,153,152,154,155,150,151,448,447,449,451,452,450,456,455,457,453,454,553,599,390,576,577,578,579,459,458,460,461,462,463,531,530,529,534,532,533,591,590,589,586,587,588,429,431,430,434,432,433,422,421,420,417,418,419,424,423,425,426,427,428,613,636,622,634,638,637,624,641,623,672,656,663,669,653,652,655,654,662,660,673 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#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, 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 2026-10-08 05:52:16 · history