Equation 677 Database

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Magma b17903430d1d…

magma b17903430d1d
Size
705
Isomorphism class hash
b17903430d1d954bb2aa1a4ce0402393132e85a03bd5c75468e8568c643c3b9f
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 20:34:04
Display reorder
660,281,52,524,346,606,282,53,522,344,604,283,51,523,345,605,280,48,527,349,609,278,49,525,347,607,279,50,526,348,608,272,58,530,352,612,273,59,528,350,610,274,57,529,351,611,54,275,533,355,615,55,276,531,353,613,56,277,532,354,614,673,686,680,684,92,152,158,28,137,93,150,156,29,135,94,151,157,27,136,91,148,154,24,140,89,149,155,25,138,90,147,153,26,139,83,143,164,34,132,84,141,162,35,133,85,142,163,33,134,146,86,160,30,131,144,87,161,31,129,145,88,159,32,130,664,666,672,670,5,174,500,464,570,3,175,498,462,568,4,176,499,463,569,0,173,503,467,573,2,171,501,465,571,1,172,502,466,572,11,165,506,470,576,9,166,504,468,574,10,167,505,469,575,168,7,509,473,579,169,8,507,471,577,170,6,508,472,578,681,685,674,682,189,112,430,203,536,190,110,428,201,534,191,111,429,202,535,192,108,433,206,539,193,109,431,204,537,194,107,432,205,538,195,115,436,209,542,196,116,434,207,540,197,114,435,208,541,653,198,654,656,657,247,199,437,210,543,113,200,438,211,544,704,701,703,699,18,512,288,476,582,19,510,289,474,580,20,511,287,475,581,21,515,284,479,585,22,513,285,477,583,23,514,286,478,584,16,518,294,482,588,17,516,295,480,586,15,517,293,481,587,521,12,290,485,591,519,13,291,483,589,520,14,292,484,590,691,694,692,693,179,594,488,67,558,177,592,486,68,556,178,593,487,66,557,182,597,491,70,561,180,595,489,71,559,181,596,490,69,560,185,600,494,65,564,183,598,492,63,562,184,599,493,64,563,603,188,497,61,567,601,186,495,62,565,602,187,496,60,566,665,667,669,663,251,308,322,356,370,252,309,320,357,368,253,310,321,358,369,250,311,325,359,373,248,312,323,360,371,249,313,324,361,372,257,314,328,362,376,258,315,326,363,374,259,316,327,364,375,317,256,331,365,379,318,254,329,366,377,319,255,330,367,378,695,690,696,689,332,406,382,263,642,333,404,380,264,640,334,405,381,265,641,335,409,385,262,645,336,407,383,260,643,337,408,384,261,644,338,412,388,269,648,339,410,386,270,646,340,411,387,271,647,415,341,391,268,651,413,342,389,266,649,414,343,390,267,650,683,688,677,675,230,77,441,547,238,231,75,439,545,236,232,76,440,546,237,233,73,444,550,241,234,74,442,548,239,235,72,443,549,240,228,81,447,553,244,229,79,445,551,242,227,80,446,552,243,658,224,659,655,652,82,225,448,554,245,78,226,449,555,246,702,698,697,700,37,218,128,98,630,38,219,126,99,628,36,220,127,100,629,40,221,124,97,633,41,222,125,95,631,39,223,123,96,632,43,216,119,104,636,44,217,117,105,634,42,215,118,106,635,212,46,122,103,639,213,47,120,101,637,214,45,121,102,638,661,671,668,662,298,452,618,394,418,296,450,616,392,416,297,451,617,393,417,301,455,621,397,421,299,453,619,395,419,300,454,620,396,420,304,458,624,400,424,302,456,622,398,422,303,457,623,399,423,461,307,627,403,427,459,305,625,401,425,460,306,626,402,426,676,678,679,687 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#c2d2ffbf4b11c3cb3cbc2e9e264bf213176e8d1ad1040891146c21601605ebcd, 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 20:34:04 · history