Equation 677 Database

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Magma 1f0aac9c135c…

magma 1f0aac9c135c
Size
705
Isomorphism class hash
1f0aac9c135cdd7cc4cbf23d2f3f437ecfd4340de8e112be0bf22d326da98ec6
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 21:11:00
Display reorder
704,205,114,220,196,206,221,197,115,204,116,219,195,216,208,117,192,217,209,118,193,218,207,119,194,226,211,202,112,227,212,203,113,225,210,201,111,214,222,198,108,215,223,199,109,213,224,200,110,183,184,185,182,180,181,189,190,187,188,186,191,674,673,675,672,594,92,600,634,595,601,635,90,596,91,602,633,603,597,95,630,604,598,93,631,605,599,94,632,606,592,625,87,607,593,626,88,608,591,624,89,588,609,628,86,589,610,629,84,590,611,627,85,620,618,619,623,621,622,615,616,613,614,612,617,666,664,667,665,128,30,73,239,126,74,237,31,127,32,72,238,76,131,33,235,77,129,34,236,75,130,35,234,79,123,230,28,80,124,228,29,78,125,229,27,122,82,233,24,120,83,231,25,121,81,232,26,648,649,650,651,652,653,654,655,658,656,657,659,685,687,684,686,359,394,367,339,357,368,340,395,358,393,366,341,370,355,390,338,371,356,391,336,369,354,392,337,365,350,345,385,363,348,346,386,364,349,347,384,353,361,344,388,351,362,342,389,352,360,343,387,373,374,372,376,377,375,379,380,381,382,383,378,700,703,701,702,461,62,472,451,459,473,452,60,460,61,471,450,468,457,65,454,469,458,63,455,470,456,64,453,478,467,449,68,479,465,447,66,477,466,448,67,463,474,445,71,464,475,446,69,462,476,444,70,484,485,483,480,481,482,490,491,488,486,487,489,688,691,689,690,307,52,315,296,308,316,294,53,306,51,317,295,314,310,48,299,312,311,49,297,313,309,50,298,321,305,291,58,322,303,292,59,323,304,293,57,301,320,290,54,302,318,288,55,300,319,289,56,330,331,332,333,334,335,328,329,326,324,325,327,662,660,663,661,529,10,501,520,530,502,521,11,528,9,503,519,500,532,6,516,498,533,7,517,499,531,8,518,492,535,526,0,493,536,527,2,494,534,525,1,538,495,522,4,539,496,523,5,537,497,524,3,507,508,509,506,504,505,513,514,511,512,510,515,694,692,695,693,242,40,258,280,240,259,281,41,241,39,260,279,261,245,36,276,262,243,37,277,263,244,38,278,256,248,286,46,257,246,287,47,255,247,285,45,251,252,282,42,249,253,283,43,250,254,284,44,267,268,269,266,264,265,273,274,271,272,270,275,681,683,680,682,574,106,587,562,575,585,563,107,573,105,586,561,583,570,102,558,584,571,103,559,582,572,104,560,578,565,553,97,576,566,554,98,577,564,552,96,568,581,556,100,569,579,557,101,567,580,555,99,548,546,547,551,549,550,543,544,541,542,540,545,697,696,699,698,421,642,435,414,422,436,415,643,420,644,437,416,434,424,645,417,432,425,646,418,433,423,647,419,441,427,412,640,442,428,413,641,443,426,411,639,430,440,408,636,431,438,409,637,429,439,410,638,406,407,405,402,403,404,397,398,399,400,401,396,671,669,670,668,138,22,146,174,139,144,175,23,140,21,145,176,149,141,18,177,147,142,19,178,148,143,20,179,152,136,172,13,150,137,173,14,151,135,171,12,132,155,168,16,133,153,169,17,134,154,170,15,166,167,165,162,163,164,157,158,159,160,161,156,676,679,677,678 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#dc3952d3945a57ff89efbf9c91902a27e7bb606727f60175866197715516bbc5, 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 21:11:01 · history