Equation 677 Database

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Magma df337f9fc16c…

magma df337f9fc16c
Size
705
Isomorphism class hash
df337f9fc16ca0f9deb07816b94ddad6f46447592ede761705bc6b0941a75332
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 16:35:49
Display reorder
704,224,29,211,199,212,222,200,27,210,28,223,198,227,214,25,202,225,215,26,203,226,213,24,201,209,35,197,219,207,33,195,220,208,34,196,221,31,205,193,218,32,206,194,216,30,204,192,217,188,186,187,191,189,190,183,184,181,182,180,185,675,673,672,674,486,135,518,509,516,487,507,136,517,137,488,508,489,521,134,505,490,519,132,506,491,520,133,504,524,141,515,484,522,142,513,485,523,143,514,483,140,527,511,480,138,525,512,481,139,526,510,482,492,493,494,495,496,497,498,499,503,501,502,500,664,666,667,665,17,47,150,231,151,15,232,45,152,46,16,233,13,153,43,230,14,154,44,228,12,155,42,229,148,38,237,23,149,36,238,21,147,37,239,22,41,144,236,19,39,145,234,20,40,146,235,18,648,649,650,651,652,653,654,655,658,656,657,659,684,686,687,685,86,100,77,62,75,84,60,101,76,99,85,61,89,73,96,65,87,74,97,63,88,72,98,64,83,106,68,92,81,107,66,90,82,105,67,91,102,79,71,95,103,80,69,93,104,78,70,94,51,52,53,50,48,49,57,58,55,56,54,59,701,703,702,700,600,576,647,635,645,601,633,577,646,578,602,634,603,643,579,631,604,644,580,632,605,642,581,630,638,582,626,606,636,583,624,607,637,584,625,608,585,641,629,609,586,639,627,610,587,640,628,611,621,622,623,620,618,619,612,613,617,615,616,614,688,689,691,690,290,156,327,314,328,288,312,157,329,158,289,313,293,326,159,317,291,324,160,315,292,325,161,316,333,162,320,296,334,163,318,294,335,164,319,295,165,332,323,299,166,330,321,297,167,331,322,298,303,304,305,302,300,301,309,310,307,308,306,311,662,661,660,663,406,115,395,431,393,407,429,116,394,114,405,430,402,391,118,427,403,392,119,428,404,390,117,426,386,113,422,397,384,111,420,398,385,112,421,396,109,389,425,400,110,387,423,401,108,388,424,399,417,418,419,416,414,415,408,409,413,411,412,410,694,693,692,695,260,588,241,278,242,258,276,589,240,590,259,277,263,244,591,281,261,245,592,279,262,243,593,280,247,594,284,255,248,595,282,256,246,596,283,257,597,250,287,254,598,251,285,252,599,249,286,253,268,269,267,264,265,266,274,275,272,270,271,273,682,683,680,681,442,122,468,462,469,443,463,120,470,121,441,464,438,471,125,465,439,472,123,466,440,473,124,467,474,128,460,433,475,126,461,434,476,127,459,432,131,477,456,436,129,478,457,437,130,479,458,435,454,455,453,450,451,452,445,446,447,448,449,444,696,698,697,699,554,8,546,529,547,552,530,6,548,7,553,528,557,549,11,532,555,550,9,533,556,551,10,531,544,3,535,560,545,4,536,558,543,5,534,559,2,540,538,563,1,541,539,561,0,542,537,562,567,568,569,566,564,565,573,574,571,572,570,575,671,668,669,670,373,168,363,352,364,374,353,169,365,170,372,351,376,362,171,348,377,360,172,349,375,361,173,350,369,174,358,379,370,175,359,380,371,176,357,378,177,368,354,382,178,366,355,383,179,367,356,381,341,339,340,337,338,336,347,345,342,343,344,346,676,678,679,677 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#35abc55380bad4d0eeaaa3ec3d1bddd8996633b3da151c70fe1eca862e930666, 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 16:35:50 · history