Equation 677 Database

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Magma 7482a2833ad0…

magma 7482a2833ad0
Size
707
Isomorphism class hash
7482a2833ad0b26bd5d191a7dde45b616cd35024272d6df2a2ff8a92b37bd76b
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 12:47:55
Display reorder
300,301,302,304,305,303,656,148,147,144,145,146,149,229,228,230,233,231,232,93,95,94,92,90,91,58,57,59,55,56,54,36,38,37,39,40,41,127,126,128,131,129,130,99,101,100,96,97,98,138,140,139,143,141,142,107,106,105,102,103,104,132,134,133,135,136,137,521,520,516,517,518,519,407,406,402,403,404,405,476,475,477,478,479,474,485,484,480,481,482,483,348,353,349,350,351,352,329,328,324,325,326,327,489,488,490,491,486,487,494,493,495,496,497,492,600,605,601,602,603,604,427,426,428,429,430,431,607,608,620,606,609,619,630,632,622,641,694,680,696,693,677,664,662,663,659,679,122,121,124,125,123,120,177,179,178,175,176,174,78,80,79,83,81,82,115,114,116,118,119,117,111,113,112,108,109,110,8,7,6,9,10,11,292,294,293,295,296,297,30,32,31,35,33,34,89,88,87,84,85,86,299,298,283,280,281,282,341,340,336,337,338,339,321,320,322,323,318,319,343,342,344,345,346,347,385,384,386,387,388,389,453,452,454,455,450,451,392,391,393,394,395,390,399,398,400,401,396,397,515,514,510,511,512,513,306,307,308,309,310,311,467,466,462,463,464,465,639,637,655,638,640,654,628,631,621,636,695,685,683,678,684,658,661,668,667,686,19,18,21,22,23,20,222,224,223,226,227,225,15,17,16,14,12,13,249,251,250,247,246,248,182,181,180,185,183,184,252,253,254,257,255,256,265,266,264,267,268,269,46,45,47,42,43,44,155,154,153,150,151,152,272,270,271,275,273,274,509,508,504,505,506,507,443,442,438,439,440,441,415,414,416,417,418,419,362,361,363,364,365,360,502,501,503,498,499,500,380,379,381,382,383,378,434,433,435,436,437,432,371,370,366,367,368,369,473,472,468,469,470,471,372,377,373,374,375,376,644,645,651,649,643,652,623,635,627,633,698,705,682,697,681,665,672,671,666,703,27,29,26,24,25,28,69,71,70,67,68,66,163,162,164,165,166,167,157,156,158,160,161,159,259,260,258,261,262,263,169,168,170,173,171,172,288,287,286,291,289,290,65,64,63,61,62,60,51,53,52,49,50,48,284,285,279,278,276,277,594,599,595,596,597,598,580,579,581,576,577,578,335,334,330,331,332,333,420,425,421,422,423,424,317,316,312,313,314,315,460,459,461,456,457,458,411,410,412,413,408,409,445,444,446,447,448,449,523,522,524,525,526,527,529,528,530,531,532,533,647,642,650,646,648,653,624,629,617,634,692,688,689,691,690,660,657,670,669,687,187,186,189,190,191,188,2,0,1,3,4,5,236,235,234,238,239,237,203,202,201,200,198,199,205,204,206,208,209,207,244,243,245,242,240,241,77,76,75,74,72,73,210,212,211,215,213,214,218,217,216,219,220,221,197,196,195,194,192,193,584,583,585,586,587,582,535,534,536,537,538,539,358,357,359,354,355,356,565,564,566,567,568,569,540,545,541,542,543,544,551,550,546,547,548,549,552,557,553,554,555,556,558,563,559,560,561,562,572,571,573,574,575,570,593,592,588,589,590,591,611,614,625,612,610,618,615,616,613,626,702,700,706,701,704,673,674,675,676,699 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#53d992532d406ee1a16d046074f6b11dc06c8f5c6df8c27dc9277719dd794878, M = {30, 31, 32, 33, 34, 35, 132} 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 12:47:57 · history