Equation 677 Database

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Magma 13cb116e0833…

magma 13cb116e0833
Size
705
Isomorphism class hash
13cb116e08335d71a37ed2dfb11d72f0a8949e19526cac2aa5c1e4fba0199e29
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 17:20:27
Display reorder
660,630,631,208,627,633,650,651,209,647,653,610,611,207,607,613,551,550,204,547,553,205,570,571,567,573,591,590,206,587,593,448,449,214,446,451,471,472,215,468,475,431,432,213,428,435,512,511,210,508,515,531,530,211,527,533,492,491,212,488,495,688,698,691,692,634,635,259,622,623,654,655,260,642,643,614,615,258,602,603,555,554,262,542,543,263,574,575,562,563,595,594,261,582,583,452,453,257,444,445,476,477,255,463,464,436,437,256,423,424,517,516,253,503,504,535,534,254,522,523,497,496,252,483,484,694,697,701,702,406,418,116,38,298,407,419,114,36,299,405,417,115,37,297,414,402,119,41,294,117,403,415,39,295,416,404,118,40,296,397,409,111,44,289,398,410,112,42,290,396,408,113,43,288,412,400,110,47,292,413,401,108,45,293,411,399,109,46,291,670,664,680,681,370,382,28,237,310,371,383,29,238,311,369,381,27,239,309,378,366,24,236,306,25,367,379,234,307,380,368,26,235,308,361,373,34,228,301,362,374,35,229,302,360,372,33,230,300,376,364,30,231,304,377,365,31,232,305,375,363,32,233,303,678,665,671,673,638,639,121,632,629,658,659,122,652,649,618,619,120,612,609,559,558,124,552,549,125,578,579,572,569,599,598,123,592,589,459,458,127,450,447,479,478,128,473,470,439,438,126,433,430,518,519,130,513,510,538,539,131,532,529,498,499,129,493,490,693,690,687,699,624,626,0,628,620,644,646,2,648,641,604,606,1,608,600,546,544,4,548,540,5,564,566,568,561,586,584,3,588,581,456,457,7,441,440,465,467,8,469,461,425,427,6,429,421,507,505,10,509,502,526,524,11,528,521,487,485,9,489,482,689,686,695,696,637,625,196,621,636,656,645,197,640,657,617,605,195,601,616,545,557,192,541,556,193,577,565,560,576,585,596,194,580,597,455,454,202,443,442,474,466,203,460,462,434,426,201,420,422,506,514,198,501,500,525,537,199,520,536,486,494,200,481,480,700,704,703,685,358,346,133,100,84,359,347,134,101,85,357,345,132,99,86,342,354,136,96,87,137,355,343,97,88,344,356,135,98,89,349,337,139,106,90,350,338,140,107,91,348,336,138,105,92,340,352,142,102,93,341,353,143,103,94,339,351,141,104,95,672,679,668,667,222,286,22,272,176,223,287,23,270,174,224,285,21,271,175,282,225,18,275,179,19,226,283,273,177,284,227,20,274,178,220,277,13,267,171,221,278,14,268,172,219,276,12,269,173,280,216,16,266,170,281,217,17,264,168,279,218,15,265,169,674,682,662,663,320,246,69,56,334,318,247,70,54,335,319,248,71,55,333,249,323,68,59,330,66,321,250,57,331,251,322,67,58,332,315,244,60,51,325,316,245,61,52,326,317,243,62,53,324,240,314,63,50,328,241,312,64,48,329,242,313,65,49,327,684,666,676,683,155,394,190,82,167,153,395,191,83,165,154,393,189,81,166,390,151,186,78,163,187,152,391,79,164,392,150,188,80,162,146,385,181,73,158,144,386,182,74,156,145,384,180,72,157,388,149,184,76,161,389,147,185,77,159,387,148,183,75,160,669,677,661,675 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#4f47b623d963c151ceba4da4fdb4170837133dc09cb743e53f258ef94ac4defc, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 17:20:28 · history