Equation 677 Database

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Magma 1c9d4a3b14b1…

magma 1c9d4a3b14b1
Size
707
Isomorphism class hash
1c9d4a3b14b103356c9e6f351efc244e77393f9a62c621365d8d6deac7182075
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 02:05:03
Display reorder
559,558,557,554,555,556,638,253,252,254,255,256,257,8,7,10,11,6,9,201,200,202,203,198,199,17,16,12,13,14,15,18,23,19,20,21,22,32,31,33,34,35,30,123,122,124,125,120,121,53,52,48,49,50,51,41,40,36,37,38,39,261,260,262,263,258,259,307,306,308,309,310,311,488,487,489,485,486,484,589,588,590,586,587,591,403,405,404,406,407,408,398,397,399,401,402,400,391,390,389,387,388,386,535,534,533,531,532,530,500,542,499,497,498,496,560,562,561,564,563,592,593,595,594,598,596,597,632,643,633,610,611,607,622,644,647,696,670,676,697,677,698,699,689,703,706,705,87,86,88,89,84,85,130,129,126,127,128,131,170,169,171,172,173,168,220,219,221,216,217,218,58,57,59,54,55,56,44,43,45,46,47,42,90,95,91,92,93,94,272,271,273,274,275,270,101,100,96,97,98,99,209,208,204,205,206,207,80,79,81,82,83,78,411,410,409,414,412,413,346,345,344,349,347,348,440,439,441,443,444,442,568,570,569,566,565,567,353,355,354,352,350,351,368,370,369,373,371,372,452,451,453,454,455,456,491,490,492,493,494,495,458,457,459,460,461,462,631,627,629,630,649,650,625,642,626,682,681,695,683,664,674,673,667,684,694,701,287,286,282,283,284,285,68,67,70,71,66,69,159,158,160,161,156,157,276,281,277,278,279,280,233,232,228,229,230,231,153,152,154,155,150,151,240,245,241,242,243,244,115,114,116,117,118,119,215,214,210,211,212,213,62,61,63,64,65,60,291,290,292,293,288,289,529,528,527,526,524,525,477,476,475,480,478,479,519,518,520,522,523,521,334,333,335,330,332,331,470,469,471,472,473,474,605,604,603,601,602,600,421,423,422,426,424,425,465,464,463,467,468,466,544,543,545,546,547,548,606,646,618,645,612,617,624,623,619,692,679,690,688,657,669,675,663,693,678,700,110,109,111,112,113,108,145,144,147,148,149,146,135,134,136,137,132,133,300,301,302,303,304,305,189,188,190,191,186,187,313,312,314,315,316,317,298,297,299,294,295,296,265,264,266,267,268,269,106,105,107,102,103,104,249,248,250,251,246,247,2,0,3,4,5,1,340,339,341,337,338,336,359,361,360,356,357,358,447,446,445,450,448,449,362,364,363,365,366,367,504,505,552,503,501,502,551,550,549,343,553,342,539,541,540,538,536,537,435,434,433,437,438,436,515,517,516,514,512,513,615,616,614,609,608,613,621,651,648,702,668,685,704,660,666,680,659,686,691,687,143,138,139,140,141,142,224,223,226,227,222,225,197,196,192,193,194,195,234,239,235,236,237,238,326,328,327,324,325,329,182,181,183,184,185,180,162,167,163,164,165,166,318,319,320,321,322,323,73,72,74,75,76,77,174,179,175,176,177,178,28,27,29,24,25,26,506,508,507,509,510,511,392,394,393,395,396,599,572,571,573,575,576,574,416,415,417,419,420,418,581,580,582,583,584,585,577,579,578,483,481,482,384,383,385,380,381,382,432,431,430,428,429,427,375,374,376,377,378,379,641,628,639,640,635,634,620,636,637,671,656,661,672,654,652,655,653,658,662,665 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#40b1db721c17bf32e266eb97cd1492697125779c7804a195f580e3a793b1a85e, 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 02:05:04 · history