Equation 677 Database

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Magma d4d999e82766…

magma d4d999e82766
Size
705
Isomorphism class hash
d4d999e827667af70d8155ae70d30087d94e3eaeb9469cf7d735950e23324d18
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 21:52:00
Display reorder
660,535,224,530,528,529,495,489,222,490,488,223,509,515,510,508,455,227,451,452,450,474,225,469,470,468,434,226,429,430,428,219,649,650,655,648,609,220,610,615,608,635,629,221,630,628,218,569,570,575,568,216,589,590,595,588,217,549,550,555,548,692,694,701,699,534,143,520,525,531,494,491,141,481,485,142,511,514,500,505,454,139,445,440,442,473,140,471,461,465,433,138,431,420,425,134,651,641,654,645,611,132,600,614,605,634,631,133,621,625,137,571,560,574,565,135,591,580,594,585,136,551,541,554,545,697,693,703,689,116,165,91,129,341,114,339,166,92,130,167,340,115,90,131,119,164,337,94,128,117,162,338,95,126,118,163,336,93,127,156,347,89,111,120,345,157,87,112,121,113,346,158,88,122,159,343,85,110,123,160,344,86,108,124,161,342,84,109,125,668,665,671,682,268,215,389,186,14,269,12,213,387,187,214,13,267,388,188,264,211,17,385,189,265,212,15,386,190,266,210,16,384,191,206,20,395,274,184,18,204,393,275,185,273,19,205,394,183,209,23,391,270,180,207,21,392,271,181,208,22,390,272,182,674,661,669,680,532,81,523,524,521,492,480,82,483,484,83,501,512,503,504,457,80,448,447,449,478,78,460,463,464,437,79,421,423,424,72,640,643,652,644,601,73,603,612,604,632,620,74,623,624,75,561,563,572,564,76,581,583,592,584,77,540,543,552,544,700,687,695,690,533,234,537,539,536,493,496,235,497,499,236,516,513,517,519,453,237,458,456,459,472,238,476,477,479,432,239,438,436,439,232,656,657,653,659,616,233,617,613,619,633,636,231,637,639,228,576,577,573,579,229,596,597,593,599,230,556,557,553,559,685,691,686,696,538,35,522,526,527,498,487,33,482,486,34,507,518,502,506,446,31,444,441,443,475,32,467,462,466,435,30,427,422,426,26,647,642,658,646,607,24,602,618,606,638,627,25,622,626,29,567,562,578,566,27,587,582,598,586,28,547,542,558,546,704,698,702,688,295,256,401,305,147,296,148,257,399,303,255,149,294,400,304,298,252,146,397,301,299,253,144,398,302,297,254,145,396,300,262,153,407,293,311,154,263,405,291,309,292,155,261,406,310,258,152,403,289,307,259,150,404,290,308,260,151,402,288,306,662,679,672,683,101,200,413,365,353,99,351,198,411,363,199,352,100,412,364,97,203,349,409,361,98,201,350,410,362,96,202,348,408,360,195,359,419,107,371,357,196,417,105,369,106,358,197,418,370,194,355,415,103,367,192,356,416,104,368,193,354,414,102,366,670,681,673,684,377,171,317,281,242,375,240,172,315,279,173,241,376,316,280,373,170,245,313,277,374,168,243,314,278,372,169,244,312,276,177,248,323,383,287,246,178,321,381,285,382,247,179,322,286,176,251,319,379,283,174,249,320,380,284,175,250,318,378,282,678,676,663,664,44,3,329,59,71,42,69,4,327,57,5,70,43,328,58,47,2,67,325,55,45,1,68,326,56,46,0,66,324,54,9,62,335,39,50,60,10,333,40,48,41,61,11,334,49,8,65,331,38,53,6,63,332,36,51,7,64,330,37,52,667,675,677,666 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#f80d3e42bb36c9de3f16a7272ddaae8a1c868ead8083a2f830ed5472d041fc61, 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 21:52:00 · history