Equation 677 Database

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Magma cec13b9933de…

magma cec13b9933de
Size
705
Isomorphism class hash
cec13b9933de586fd31663b4534428723343faa82019af63b9496e912e571d79
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 19:58:57
Display reorder
660,512,511,510,514,515,513,509,507,508,505,506,504,289,290,288,292,293,291,295,296,294,298,299,297,571,572,570,574,575,573,569,567,568,565,566,564,452,450,451,455,453,454,447,448,449,446,444,445,201,202,203,200,198,199,192,193,194,195,196,197,665,662,667,677,645,647,646,643,644,642,638,636,637,641,639,640,367,368,366,370,371,369,365,363,364,361,362,360,21,22,23,20,18,19,12,13,14,15,16,17,111,112,113,110,108,109,117,118,119,116,114,115,82,83,81,78,79,80,73,74,72,76,77,75,687,684,690,696,535,534,536,537,538,539,532,533,531,528,529,530,591,592,593,590,588,589,597,598,599,596,594,595,474,475,476,477,478,479,472,473,471,468,469,470,419,417,418,415,416,414,410,408,409,413,411,412,160,161,159,156,157,158,166,167,165,162,163,164,664,663,668,670,658,657,659,656,654,655,648,649,650,651,652,653,394,395,393,390,391,392,385,386,384,388,389,387,378,379,380,381,382,383,376,377,375,372,373,374,7,8,6,10,11,9,5,3,4,0,2,1,126,127,128,129,130,131,124,125,123,120,121,122,675,678,681,683,301,300,302,303,304,305,306,307,308,309,310,311,331,332,330,334,335,333,329,327,328,325,326,324,312,313,314,315,316,317,318,319,320,321,322,323,140,138,139,143,141,142,135,136,137,134,132,133,399,400,401,398,396,397,405,406,407,404,402,403,666,661,669,671,520,519,521,518,516,517,525,526,527,524,522,523,581,579,580,577,578,576,587,585,586,583,584,582,155,153,154,151,152,150,146,144,145,149,147,148,50,48,49,53,51,52,56,54,55,59,57,58,461,459,460,457,458,456,467,465,466,463,464,462,694,692,697,702,228,230,229,233,231,232,236,234,235,239,237,238,245,243,244,241,242,240,251,249,250,247,248,246,257,255,256,253,254,252,263,261,262,259,260,258,214,215,213,210,211,212,205,206,204,208,209,207,227,225,226,223,224,222,218,216,217,221,219,220,700,699,703,704,342,344,343,347,345,346,339,340,341,338,336,337,36,37,38,39,40,41,42,43,44,45,46,47,623,621,622,619,620,618,614,612,613,617,615,616,86,84,85,89,87,88,92,90,91,95,93,94,25,26,24,28,29,27,31,32,30,34,35,33,695,693,698,701,502,501,503,500,498,499,492,493,494,495,496,497,286,287,285,282,283,284,277,278,276,280,281,279,266,264,265,269,267,268,272,270,271,275,273,274,433,434,432,436,437,435,439,440,438,442,443,441,561,562,563,560,558,559,552,553,554,555,556,557,674,672,679,682,178,177,179,176,174,175,168,169,170,171,172,173,106,107,105,102,103,104,97,98,96,100,101,99,181,182,180,184,185,183,187,188,186,190,191,189,357,358,359,356,354,355,348,349,350,351,352,353,631,632,630,634,635,633,629,627,628,625,626,624,676,673,680,686,601,600,602,603,604,605,606,607,608,609,610,611,423,424,425,422,420,421,429,430,431,428,426,427,481,482,480,484,485,483,487,488,486,490,491,489,61,62,60,64,65,63,67,68,66,70,71,69,542,540,541,545,543,544,548,546,547,551,549,550,688,685,689,691 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, 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 19:58:58 · history