Equation 677 Database

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Magma f6c8d1ba928c…

magma f6c8d1ba928c
Size
705
Isomorphism class hash
f6c8d1ba928c476cac3ef80b722f9f7e6cdd79a418e5c4641ef1ce8858934afd
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 21:09:26
Display reorder
704,333,347,86,321,334,345,84,322,335,346,85,323,332,89,343,320,330,344,318,87,331,88,342,319,312,324,338,92,313,325,336,90,326,314,337,91,315,327,341,95,316,328,339,93,317,329,340,94,310,311,309,306,307,308,301,302,303,304,305,300,674,673,675,672,560,570,430,594,558,571,431,595,559,572,429,596,563,426,573,597,561,574,598,427,562,428,575,599,592,555,568,421,593,556,569,422,557,591,567,420,588,554,564,424,589,552,565,425,590,553,566,423,582,583,584,585,586,587,580,581,578,576,577,579,666,664,667,665,82,70,98,224,83,71,96,222,81,69,97,223,78,101,66,227,79,67,225,99,80,100,68,226,219,73,61,104,220,74,62,102,72,221,60,103,218,76,64,107,216,77,65,105,217,75,63,106,648,649,650,651,652,653,654,655,658,656,657,659,685,687,684,686,28,40,4,16,29,41,5,17,27,39,3,15,24,1,36,12,25,37,13,0,26,2,38,14,22,34,46,10,23,35,47,11,33,21,45,9,18,30,42,6,19,31,43,7,20,32,44,8,52,53,51,48,49,50,58,59,56,54,55,57,700,703,701,702,453,465,358,489,454,466,359,490,455,467,357,491,452,354,464,488,450,462,486,355,451,356,463,487,480,444,456,349,481,445,457,350,446,482,458,348,483,447,459,352,484,448,460,353,485,449,461,351,478,479,477,474,475,476,469,470,471,472,473,468,688,691,689,690,128,140,276,160,126,138,277,161,127,139,278,159,131,279,143,156,129,141,157,280,130,281,142,158,166,123,135,282,167,124,136,283,125,165,137,284,162,122,134,285,163,120,132,286,164,121,133,287,152,150,151,155,153,154,147,148,145,146,144,149,662,660,663,661,393,405,501,381,394,406,502,382,395,407,503,383,392,500,404,380,390,402,378,498,391,499,403,379,372,384,396,492,373,385,397,493,386,374,398,494,375,387,399,495,376,388,400,496,377,389,401,497,370,371,369,366,367,368,361,362,363,364,365,360,694,692,695,693,254,266,111,242,252,264,112,240,253,265,113,241,257,110,269,245,255,267,243,108,256,109,268,244,248,260,272,117,246,258,270,118,259,247,271,119,251,263,275,116,249,261,273,114,250,262,274,115,228,229,230,231,232,233,234,235,239,237,238,236,681,683,680,682,531,542,412,521,532,540,413,519,533,541,411,520,530,408,545,517,528,543,518,409,529,410,544,516,527,537,548,418,525,538,546,419,539,526,547,417,523,536,551,414,524,534,549,415,522,535,550,416,509,507,508,505,506,504,515,513,510,511,512,514,697,696,699,698,632,642,439,620,630,643,440,618,631,644,438,619,635,442,645,623,633,646,621,443,634,441,647,622,615,627,640,437,616,628,641,435,629,617,639,436,614,626,636,433,612,624,637,434,613,625,638,432,606,607,608,609,610,611,604,605,602,600,601,603,671,669,670,668,183,194,288,175,184,192,289,176,185,193,290,174,182,291,197,178,180,195,179,292,181,293,196,177,173,189,200,294,171,190,198,295,191,172,199,296,169,188,203,297,170,186,201,298,168,187,202,299,206,204,205,209,207,208,212,210,214,215,213,211,676,679,677,678 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#d999f02d519da9e6482c93589338b3231f65cc1ce6e36c19968e5d782b765397, 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 21:09:26 · history