Equation 677 Database

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Magma 6951d89ab4f6…

magma 6951d89ab4f6
Size
707
Isomorphism class hash
6951d89ab4f69d74d815941ec64ce2dc7696649a3b315ba17e5987ee7c4a4261
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 17:10:18
Display reorder
305,304,303,300,302,301,656,17,16,13,14,12,15,63,65,64,61,62,60,24,26,25,29,27,28,38,37,36,41,39,40,44,43,42,47,45,46,32,31,30,35,33,34,19,18,20,23,21,22,192,194,193,195,196,197,88,87,89,86,84,85,80,79,78,83,81,82,557,556,552,553,554,555,311,310,307,306,308,309,499,498,500,501,502,503,584,583,585,586,587,582,570,575,571,572,573,574,354,359,355,356,357,358,386,385,387,388,389,384,605,604,600,601,602,603,414,419,415,416,417,418,472,471,473,468,469,470,606,609,616,607,608,618,647,615,626,643,700,677,672,701,663,667,702,660,658,699,73,72,75,76,77,74,126,128,127,130,131,129,234,236,235,239,237,238,135,137,136,132,133,134,92,91,90,95,93,94,143,142,141,140,138,139,52,51,53,50,48,49,269,268,267,266,265,264,66,68,67,70,71,69,299,298,295,292,293,294,333,332,334,335,330,331,375,374,376,377,372,373,488,487,489,490,491,486,492,497,493,494,495,496,322,321,323,318,319,320,561,560,562,563,558,559,551,550,546,547,548,549,413,412,408,409,410,411,429,428,430,431,426,427,405,404,406,407,402,403,641,648,655,638,636,650,642,621,627,635,688,678,671,692,668,665,691,661,669,687,10,9,6,7,8,11,0,1,2,5,3,4,244,243,245,240,241,242,215,214,213,212,210,211,55,54,56,58,59,57,156,157,158,160,161,159,164,162,163,165,166,167,287,286,285,284,283,282,119,118,117,114,115,116,277,278,276,279,280,281,362,361,363,364,365,360,534,539,535,536,537,538,593,592,588,589,590,591,347,346,342,343,344,345,424,423,425,420,421,422,596,595,597,598,599,594,443,442,438,439,440,441,450,455,451,452,453,454,449,448,444,445,446,447,577,576,578,579,580,581,646,639,653,637,634,652,631,622,628,630,690,686,679,694,675,676,693,673,674,689,251,250,247,248,246,249,173,172,171,168,169,170,149,148,147,145,146,144,184,183,185,180,182,181,190,189,191,186,188,187,155,154,153,152,150,151,203,202,201,198,199,200,275,274,273,272,270,271,125,124,123,120,121,122,296,297,291,290,288,289,336,341,337,338,339,340,328,327,329,324,325,326,481,480,482,483,484,485,545,544,540,541,542,543,432,437,433,434,435,436,391,390,392,393,394,395,370,369,371,366,367,368,568,567,569,564,565,566,349,348,350,351,352,353,383,382,378,379,380,381,645,640,654,644,649,651,629,617,632,633,696,662,666,697,670,664,698,659,657,695,221,220,217,218,216,219,97,96,98,101,99,100,256,255,257,253,252,254,110,109,108,113,111,112,103,102,104,106,107,105,231,233,232,228,229,230,223,222,224,227,225,226,263,262,261,260,259,258,176,175,174,177,178,179,208,207,209,205,206,204,518,517,519,520,521,516,529,528,530,531,532,533,459,458,460,461,456,457,522,527,523,524,525,526,478,477,479,474,475,476,466,465,467,462,463,464,513,512,514,515,510,511,401,400,396,397,398,399,313,312,314,315,316,317,508,507,509,504,505,506,611,612,623,610,613,624,620,614,625,619,706,683,685,703,684,680,704,681,682,705 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 = {48, 49, 50, 51, 52, 53, 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 2026-10-08 17:10:19 · history