Equation 677 Database

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Magma 19e13e16fbf3…

magma 19e13e16fbf3
Size
705
Isomorphism class hash
19e13e16fbf3d37d6d067e55844421d2bc2953361c34cb26b3d9f2a3d819519b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 16:46:10
Display reorder
660,293,292,291,288,289,290,298,299,297,294,295,296,334,153,154,335,155,333,152,330,150,331,151,332,144,325,145,326,146,324,147,328,148,329,149,327,315,301,316,302,317,300,314,304,312,305,313,303,321,307,322,308,323,306,320,310,318,311,319,309,676,685,679,689,453,455,454,451,452,450,446,444,445,449,447,448,440,18,19,438,20,439,21,443,22,441,23,442,16,435,17,436,15,437,12,434,13,432,14,433,427,464,428,462,426,463,430,467,431,465,429,466,425,459,423,460,424,461,421,458,422,456,420,457,687,699,695,703,138,140,139,143,141,142,135,136,137,134,132,133,129,282,283,130,284,131,285,128,286,126,287,127,280,120,281,121,279,122,276,123,277,124,278,125,111,107,112,105,113,106,110,103,108,104,109,102,117,98,118,96,119,97,116,101,114,99,115,100,664,671,670,682,482,481,480,484,485,483,487,488,486,490,491,489,473,173,171,471,172,472,169,469,170,470,168,468,179,479,177,477,178,478,175,475,176,476,174,474,508,503,509,501,507,502,504,499,505,500,506,498,514,494,515,492,513,493,510,497,511,495,512,496,674,683,680,688,193,192,194,195,196,197,198,199,200,201,202,203,185,46,47,183,45,184,42,181,43,182,44,180,37,191,38,189,36,190,40,187,41,188,39,186,158,521,156,519,157,520,161,517,159,518,160,516,164,527,162,525,163,526,167,523,165,524,166,522,693,697,694,701,590,589,588,592,593,591,595,596,594,598,599,597,579,56,54,580,55,581,59,578,57,576,58,577,51,585,52,586,53,587,50,584,48,582,49,583,252,611,253,609,254,610,255,607,256,608,257,606,258,602,259,600,260,601,261,605,262,603,263,604,692,700,691,702,245,244,243,240,241,242,250,251,249,246,247,248,228,35,33,229,34,230,31,231,32,232,30,233,26,234,24,235,25,236,29,237,27,238,28,239,224,204,222,205,223,206,227,207,225,208,226,209,219,210,220,211,221,212,218,213,216,214,217,215,661,663,662,668,348,350,349,353,351,352,356,354,355,359,357,358,340,10,11,341,9,339,6,336,7,337,8,338,0,346,2,347,1,345,4,342,5,343,3,344,64,367,65,368,63,366,60,370,61,371,62,369,70,365,71,363,69,364,66,361,67,362,68,360,675,684,678,690,643,642,644,645,646,647,640,641,639,636,637,638,634,275,273,635,274,633,271,630,272,631,270,632,266,625,264,626,265,624,269,628,267,629,268,627,623,654,621,655,622,656,619,657,620,658,618,659,614,652,612,653,613,651,617,648,615,649,616,650,686,698,696,704,556,555,557,554,552,553,561,562,563,560,558,559,540,80,78,541,79,542,83,543,81,544,82,545,75,546,76,547,77,548,74,549,72,550,73,551,536,566,534,564,535,565,539,569,537,567,538,568,531,572,532,570,533,571,530,575,528,573,529,574,666,672,665,677,414,416,415,419,417,418,411,412,413,410,408,409,405,92,90,406,91,407,95,404,93,402,94,403,87,396,88,397,89,398,86,399,84,400,85,401,395,381,393,382,394,383,391,380,392,378,390,379,386,372,384,373,385,374,389,375,387,376,388,377,667,673,669,681 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {62} in E, B = magma#15fbff501c8b89769a455d502d124c300eee5410941b1d2c6635f2cbb99c8e39. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 16:46:11 · history