Equation 677 Database

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Magma 355b31b370e3…

magma 355b31b370e3
Size
705
Isomorphism class hash
355b31b370e377afcb5d4230c7b5a1c272b05e6dd07ff4b03c7d04d6cca78e3a
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 17:42:50
Display reorder
660,6,191,508,60,19,7,20,189,509,61,8,18,190,507,62,187,9,22,504,63,188,10,23,505,64,186,11,21,506,65,514,197,4,17,58,195,5,15,515,59,196,3,16,513,57,1,193,13,510,54,0,194,14,511,55,2,192,12,512,56,686,678,683,679,442,148,372,418,409,443,410,149,373,419,441,408,147,374,417,144,438,412,375,414,145,439,413,376,415,146,440,411,377,416,370,139,448,407,424,140,449,405,371,425,138,447,406,369,423,444,142,403,366,420,445,143,404,367,421,446,141,402,368,422,663,667,662,665,472,158,430,526,382,473,383,156,431,527,471,381,157,429,525,161,468,378,426,522,159,469,379,427,523,160,470,380,428,524,436,153,478,388,532,154,479,389,437,533,155,477,387,435,531,474,152,384,432,528,475,150,385,433,529,476,151,386,434,530,677,674,680,675,518,118,38,339,332,516,330,119,36,340,517,331,117,37,341,114,521,335,41,338,115,519,333,39,336,116,520,334,40,337,644,124,647,648,645,125,655,656,652,653,123,639,640,637,636,612,120,613,617,616,623,121,624,621,620,631,122,632,629,628,704,699,703,698,394,202,358,538,484,395,485,203,359,539,393,483,201,357,537,198,390,480,354,534,199,391,481,355,535,200,392,482,356,536,364,208,400,490,544,209,401,491,365,545,207,399,489,363,543,396,204,486,360,540,397,205,487,361,541,398,206,488,362,542,691,692,693,690,107,322,27,454,550,105,551,323,28,455,106,549,321,29,453,318,103,546,26,450,319,104,547,24,451,320,102,548,25,452,33,328,113,556,460,329,111,557,34,461,327,112,555,35,459,109,324,552,32,456,110,325,553,30,457,108,326,554,31,458,661,670,664,668,268,84,281,305,293,269,291,85,279,303,267,292,86,280,304,87,264,289,277,301,88,265,290,278,302,89,266,288,276,300,272,82,259,284,296,83,260,282,270,294,81,258,283,271,295,262,78,287,275,299,263,79,285,273,297,261,80,286,274,298,695,694,696,689,586,100,311,568,604,587,605,101,309,569,585,603,99,310,567,96,582,600,307,564,97,583,601,308,565,98,584,602,306,566,317,91,592,610,574,92,593,611,315,575,90,591,609,316,573,588,94,606,313,570,589,95,607,314,571,590,93,608,312,572,685,688,682,673,580,172,598,562,465,581,466,173,599,563,579,467,171,597,561,168,576,464,594,558,169,577,462,595,559,170,578,463,596,560,651,163,650,646,649,164,658,654,659,657,162,642,638,643,641,619,166,618,615,614,626,167,622,627,625,634,165,630,635,633,701,697,700,702,129,73,49,346,496,130,497,74,50,347,131,495,72,48,345,76,128,492,52,342,77,126,493,53,343,75,127,494,51,344,47,71,135,502,352,69,136,503,45,353,70,137,501,46,351,134,67,498,43,348,132,68,499,44,349,133,66,500,42,350,671,666,672,669,235,178,246,224,211,236,212,179,247,222,234,210,177,248,223,174,238,214,249,227,175,239,215,250,225,176,237,213,251,226,252,184,241,217,230,185,242,218,253,228,183,240,216,254,229,244,180,220,255,233,245,181,221,256,231,243,182,219,257,232,687,681,676,684 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#6086f0079822f3fde2aa4f203419cd6117656c7d05938f081a69b332c89c02c3, 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 17:42:51 · history