Equation 677 Database

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Magma 5cbdb6f2f2e8…

magma 5cbdb6f2f2e8
Size
707
Isomorphism class hash
5cbdb6f2f2e86da99118f9792af8efc0c546911e581edd7b6f01e9ae7327d9ee
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 01:06:04
Display reorder
448,447,443,444,445,446,683,212,211,210,215,213,214,207,209,208,205,206,204,93,95,94,92,91,90,197,196,195,194,192,193,225,227,226,224,222,223,183,185,184,180,181,182,88,87,89,85,84,86,202,201,203,199,200,198,141,143,142,139,140,138,220,219,221,218,216,217,189,191,190,187,188,186,435,434,436,431,432,433,442,441,437,438,439,440,346,345,347,342,343,344,410,409,411,412,407,408,353,352,348,349,350,351,450,449,451,452,453,454,458,457,459,460,455,456,563,562,564,565,596,591,593,597,592,595,594,566,636,626,640,635,641,634,637,639,620,619,638,706,697,705,677,673,682,668,666,663,179,178,177,176,174,175,27,29,28,25,26,24,14,13,12,16,17,15,82,81,83,79,80,78,22,21,23,18,19,20,235,234,236,238,239,237,246,248,247,251,249,250,287,286,285,284,282,283,290,289,288,291,292,293,314,313,312,315,316,317,272,271,270,273,274,275,601,600,598,599,537,538,396,395,397,398,399,400,401,406,402,403,404,405,502,501,497,498,499,500,354,359,355,356,357,358,380,379,375,376,377,378,540,539,541,576,577,578,587,590,588,589,558,559,527,526,528,529,530,575,618,654,658,651,614,644,653,632,647,608,609,687,671,699,662,693,684,696,694,661,66,68,67,69,70,71,52,51,53,50,48,49,62,61,60,64,65,63,57,59,58,54,55,56,166,165,167,162,163,164,278,277,276,281,279,280,114,116,115,119,117,118,303,305,304,301,300,302,73,72,74,77,75,76,269,268,267,264,265,266,150,152,151,154,155,153,547,546,543,542,544,545,469,468,470,471,472,467,331,335,330,332,333,334,420,419,421,422,423,424,363,362,364,365,360,361,426,425,427,428,429,430,556,555,557,585,586,584,583,582,580,581,553,554,522,521,523,524,525,574,612,615,650,627,629,652,656,613,623,625,611,688,692,695,686,685,698,665,670,674,255,257,256,252,253,254,157,156,158,161,159,160,105,107,106,104,102,103,308,306,307,311,309,310,120,122,121,125,123,124,9,11,10,6,7,8,98,97,96,100,101,99,242,241,240,245,243,244,172,171,173,170,168,169,329,328,327,324,326,325,229,228,230,233,231,232,602,605,603,604,560,561,510,509,511,512,513,514,383,382,384,385,386,381,488,487,489,490,485,486,507,506,508,503,504,505,483,482,484,479,480,481,367,366,368,567,568,569,571,570,572,573,393,394,549,548,550,551,552,579,657,631,660,642,624,607,645,648,621,622,628,691,690,676,669,700,689,664,672,667,40,39,41,37,38,36,129,131,130,127,128,126,45,47,46,44,42,43,137,136,135,134,132,133,323,322,321,319,320,318,295,294,296,298,299,297,32,31,30,34,35,33,0,1,2,4,5,3,112,111,113,110,108,109,148,147,149,146,144,145,262,261,263,260,258,259,495,494,496,491,492,493,388,387,389,390,391,392,374,373,369,370,371,372,520,519,515,516,517,518,339,338,340,341,336,337,531,532,533,534,535,536,416,415,417,418,413,414,475,474,476,477,478,473,463,462,464,465,466,461,643,646,633,649,659,655,606,610,616,617,630,680,679,681,704,701,703,702,678,675 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = {108, 109, 110, 111, 112, 113, 138} 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 01:06:05 · history