Equation 677 Database

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Magma 22d028e467b8…

magma 22d028e467b8
Size
705
Isomorphism class hash
22d028e467b82d92d6bedaf96a30655bd80d93bfbd94d600473cfbe3e61eb6ff
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 16:28:58
Display reorder
660,99,175,497,110,40,100,176,108,498,41,101,177,109,496,39,174,98,113,500,36,172,96,111,501,37,173,97,112,499,38,105,503,181,116,46,106,504,182,114,47,107,502,183,115,45,506,104,180,119,42,507,102,178,117,43,505,103,179,118,44,668,672,666,661,422,60,509,425,254,423,61,426,510,255,421,62,424,508,253,63,418,428,512,250,64,419,429,513,251,65,420,427,511,252,413,515,66,431,245,414,516,67,432,246,412,514,68,430,244,518,416,69,434,248,519,417,70,435,249,517,415,71,433,247,688,687,685,686,401,303,485,437,197,402,301,438,486,198,400,302,436,484,196,299,404,440,488,200,300,405,441,489,201,298,403,439,487,199,407,491,294,443,203,408,492,292,444,204,406,490,293,442,202,494,410,297,446,206,495,411,295,447,207,493,409,296,445,205,667,665,669,663,449,81,377,601,261,450,82,602,378,259,448,83,600,376,260,80,452,604,380,257,78,453,605,381,258,79,451,603,379,256,455,383,72,607,267,456,384,73,608,265,454,382,74,606,266,386,458,75,610,263,387,459,76,611,264,385,457,77,609,262,675,682,680,676,389,35,577,269,533,390,33,270,578,534,388,34,268,576,532,31,392,272,580,536,32,393,273,581,537,30,391,271,579,535,395,583,26,275,539,396,584,24,276,540,394,582,25,274,538,586,398,29,278,542,587,399,27,279,543,585,397,28,277,541,671,664,670,662,521,187,565,7,621,522,188,8,566,622,520,189,6,564,620,186,524,10,568,624,184,525,11,569,625,185,523,9,567,623,527,571,193,5,627,528,572,194,3,628,526,570,195,4,626,574,530,192,0,630,575,531,190,2,631,573,529,191,1,629,698,695,700,696,614,130,147,133,557,615,131,134,145,558,613,129,132,146,556,126,617,136,143,560,127,618,137,144,561,128,616,135,142,559,612,141,121,139,563,647,645,122,644,646,619,140,120,138,562,653,655,124,652,654,656,659,125,657,658,649,651,123,648,650,702,703,701,704,285,14,345,461,333,283,12,462,343,331,284,13,460,344,332,17,281,464,341,329,15,282,465,342,330,16,280,463,340,328,291,351,20,467,339,289,349,18,468,337,290,350,19,466,338,347,287,23,470,335,348,288,21,471,336,346,286,22,469,334,699,694,693,697,162,240,158,473,214,160,238,474,159,215,161,239,472,157,216,243,165,476,154,217,241,163,477,155,218,242,164,475,156,219,168,149,235,479,212,166,150,236,480,213,167,148,237,478,211,152,171,234,482,208,153,169,232,483,209,151,170,233,481,210,679,677,681,684,91,52,365,633,355,92,53,634,366,356,90,51,632,364,357,48,94,636,368,354,49,95,637,369,352,50,93,635,367,353,89,371,58,639,361,87,372,59,640,362,88,370,57,638,363,374,85,54,642,360,375,86,55,643,358,373,84,56,641,359,674,683,673,678,589,227,545,312,321,590,228,310,546,319,588,226,311,544,320,230,592,315,548,317,231,593,313,549,318,229,591,314,547,316,595,551,225,307,327,596,552,223,308,325,594,550,224,309,326,554,598,221,306,323,555,599,222,304,324,553,597,220,305,322,689,692,691,690 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#33430dadf8546adceaddacfc75eeb6c00258f5413ce1926e16e948db7c79b4f3, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:28:59 · history