Equation 677 Database

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Magma 179c0aa1248f…

magma 179c0aa1248f
Size
705
Isomorphism class hash
179c0aa1248f5ecccf483456431cf478fe8469f26c136c4ee9c65ea7c85db92b
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 15:24:34
Display reorder
704,588,602,589,590,591,592,593,594,595,596,597,598,599,600,601,574,575,576,577,578,579,580,581,582,583,584,585,586,587,573,551,552,553,554,555,556,557,543,544,545,546,547,548,549,571,572,558,559,560,561,562,563,564,565,566,567,568,569,570,550,675,674,672,673,157,156,158,159,160,161,162,163,164,165,166,167,153,154,155,180,181,182,168,169,170,171,172,173,174,175,176,177,178,179,139,140,141,142,143,144,145,146,147,148,149,150,151,152,128,129,130,131,132,133,134,135,136,137,123,124,125,126,127,138,665,664,666,667,616,615,617,603,604,605,606,607,608,609,610,611,612,613,614,621,622,623,624,625,626,627,628,629,630,631,632,618,619,620,650,651,652,653,654,655,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,2,1,0,658,659,657,656,685,686,687,684,13,12,14,15,16,17,3,4,5,6,7,8,9,10,11,24,25,26,27,28,29,30,31,32,18,19,20,21,22,23,36,37,38,39,40,41,42,43,44,45,46,47,33,34,56,57,58,59,60,61,62,48,49,50,51,52,53,54,55,35,703,702,701,700,246,245,247,248,249,250,251,252,253,254,255,256,257,243,244,266,267,268,269,270,271,272,258,259,260,261,262,263,264,265,287,273,274,275,276,277,278,279,280,281,282,283,284,285,295,296,297,298,299,300,301,302,288,289,290,291,292,293,294,286,688,689,691,690,482,481,468,469,470,471,472,473,474,475,476,477,478,479,480,465,466,467,453,454,455,456,457,458,459,460,461,462,463,464,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,423,662,661,660,663,305,304,306,307,308,309,310,311,312,313,314,315,316,317,303,322,323,324,325,326,327,328,329,330,331,332,318,319,320,321,340,341,342,343,344,345,346,347,333,334,335,336,337,338,357,358,359,360,361,362,348,349,350,351,352,353,354,355,356,339,694,695,692,693,408,422,409,410,411,412,413,414,415,416,417,418,419,420,421,394,395,396,397,398,399,400,401,402,403,404,405,406,407,393,371,372,373,374,375,376,377,363,364,365,366,367,368,369,391,392,378,379,380,381,382,383,384,385,386,387,388,389,390,370,681,680,682,683,68,67,69,70,71,72,73,74,75,76,77,63,64,65,66,79,80,81,82,83,84,85,86,87,88,89,90,91,92,78,106,107,93,94,95,96,97,98,99,100,101,102,103,104,111,112,113,114,115,116,117,118,119,120,121,122,108,109,110,105,698,697,696,699,213,227,214,215,216,217,218,219,220,221,222,223,224,225,226,239,240,241,242,228,229,230,231,232,233,234,235,236,237,238,201,202,203,204,205,206,207,208,209,210,211,212,198,199,196,197,183,184,185,186,187,188,189,190,191,192,193,194,195,200,671,670,669,668,497,496,483,484,485,486,487,488,489,490,491,492,493,494,495,505,506,507,508,509,510,511,512,498,499,500,501,502,503,504,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,513,676,677,678,679 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#17d8eb76b6bf5b6d0c7c94cbffab8bf30c3f61585a1079f6e7ebccc76f8bf7d1, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 15:24:36 · history