Equation 677 Database

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Magma 93ee000a283a…

magma 93ee000a283a
Size
705
Isomorphism class hash
93ee000a283a95b68c212ea624dda4df99652377ea0b3505933fc708d63a4305
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 16:54:53
Display reorder
660,310,207,191,150,134,311,148,205,192,135,312,149,206,190,133,313,203,146,194,137,314,204,147,195,138,315,202,145,193,136,198,141,189,308,132,196,139,187,309,130,197,140,188,307,131,144,201,185,304,128,142,199,186,305,129,143,200,184,306,127,669,672,665,662,7,451,64,367,448,8,368,452,65,453,9,369,450,66,449,10,456,366,63,457,11,458,364,61,459,12,455,365,62,454,463,373,55,13,462,465,374,56,14,464,461,375,57,15,460,372,469,58,16,468,370,471,59,17,470,371,467,60,18,466,687,686,685,692,223,425,329,319,621,224,320,426,330,622,225,321,424,328,620,222,428,318,332,624,220,429,316,333,625,221,427,317,331,623,431,325,335,229,627,432,326,336,230,628,430,327,334,231,626,324,434,338,228,630,322,435,339,226,631,323,433,337,227,629,667,671,666,661,274,341,541,589,413,275,590,342,542,414,276,588,340,540,412,277,344,592,544,416,278,345,593,545,417,279,343,591,543,415,347,595,547,272,419,348,596,548,273,420,346,594,546,271,418,598,350,550,268,422,599,351,551,269,423,597,349,549,270,421,674,676,682,679,281,377,517,565,245,282,566,378,518,246,280,564,376,516,244,284,380,568,520,248,285,381,569,521,249,283,379,567,519,247,383,571,523,287,251,384,572,524,288,252,382,570,522,286,250,574,386,526,290,254,575,387,527,291,255,573,385,525,289,253,663,664,670,668,36,505,609,208,481,34,209,506,610,482,35,210,504,608,480,32,508,211,612,484,33,509,212,613,485,31,507,213,611,483,511,214,615,42,487,512,215,616,40,488,510,216,614,41,486,217,514,618,38,490,218,515,619,39,491,219,513,617,37,489,696,694,697,700,159,602,167,473,2,157,474,603,168,3,158,472,601,166,0,162,605,476,163,5,160,606,477,164,6,161,604,475,165,4,600,479,170,154,1,647,646,644,155,645,607,478,169,156,171,654,655,652,153,653,658,659,656,151,657,650,651,649,152,648,703,704,701,702,297,553,264,493,72,295,494,554,262,70,296,492,552,263,71,293,556,496,267,68,294,557,497,265,69,292,555,495,266,67,559,499,259,303,78,560,500,260,301,76,558,498,261,302,77,502,562,258,299,74,503,563,256,300,75,501,561,257,298,73,698,693,695,699,173,110,52,394,124,174,395,111,53,125,172,396,109,54,126,176,113,397,51,123,177,114,398,49,121,175,112,399,50,122,108,392,43,179,115,106,393,44,180,116,107,391,45,178,117,388,104,46,182,118,389,105,47,183,119,390,103,48,181,120,681,678,680,684,26,446,356,401,633,27,402,447,357,634,25,400,445,355,632,29,442,404,352,636,30,443,405,353,637,28,444,403,354,635,437,407,362,24,639,438,408,363,22,640,436,406,361,23,638,410,440,358,20,642,411,441,359,21,643,409,439,360,19,641,673,683,675,677,232,83,577,529,100,233,530,84,578,101,234,528,82,576,102,235,79,532,580,99,236,80,533,581,97,237,81,531,579,98,89,535,583,238,91,90,536,584,239,92,88,534,582,240,93,538,85,586,241,94,539,86,587,242,95,537,87,585,243,96,688,691,689,690 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#48377dacddf39e37ac6c06158aa2a2d147d932b71f91ecfb6a61a025238f8f4a, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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 16:54:54 · history