Equation 677 Database

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Magma e84f1708eaaf…

magma e84f1708eaaf
Size
705
Isomorphism class hash
e84f1708eaaf45cd88afe2142a19e3551ab553e06a5a960cd745cd62bac21dd5
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 18:16:58
Display reorder
660,290,57,422,100,362,291,58,423,98,363,289,56,421,99,361,60,286,418,103,358,287,61,419,101,359,59,288,420,102,360,413,281,63,95,353,414,282,64,96,354,412,280,62,97,352,284,416,66,94,356,285,417,67,92,357,283,415,65,93,355,687,679,682,675,168,127,458,248,243,166,125,459,249,241,167,126,457,247,242,123,171,454,244,239,169,124,455,245,240,122,170,456,246,238,449,163,118,254,234,450,164,116,255,232,448,165,117,253,233,162,452,121,250,237,160,453,119,251,235,161,451,120,252,236,672,661,665,662,314,109,470,526,550,315,107,471,527,551,313,108,469,525,549,105,310,466,522,546,311,106,467,523,547,104,312,468,524,548,461,305,115,517,541,462,306,113,518,542,460,304,114,516,540,308,464,111,520,544,309,465,112,521,545,307,463,110,519,543,685,686,683,677,647,0,648,644,650,655,2,656,653,658,639,1,640,636,642,4,615,616,612,618,623,5,624,620,626,3,631,632,629,634,485,146,7,29,565,486,147,8,30,566,484,145,6,31,564,597,598,10,600,601,607,608,11,605,610,144,487,9,24,567,703,700,697,704,72,190,434,326,482,73,191,435,327,483,71,192,433,325,481,193,68,430,322,478,69,194,431,323,479,195,70,432,324,480,425,78,188,317,473,426,79,189,318,474,424,77,187,316,472,74,428,184,320,476,75,429,185,321,477,76,427,186,319,475,690,693,691,689,562,51,410,12,538,563,52,411,13,539,561,50,409,14,537,54,558,406,15,534,559,55,407,16,535,53,560,408,17,536,401,553,49,18,529,402,554,47,19,530,400,552,48,20,528,556,404,45,21,532,557,405,46,22,533,555,403,44,23,531,666,668,664,669,202,275,218,446,138,203,276,219,447,139,204,274,217,445,137,278,205,214,442,134,206,279,215,443,135,277,207,216,444,136,209,200,273,437,129,210,201,271,438,130,208,199,272,436,128,196,212,269,440,132,197,213,270,441,133,198,211,268,439,131,692,695,696,694,42,85,374,498,594,43,83,375,499,595,41,84,373,497,593,81,38,370,494,590,39,82,371,495,591,80,40,372,496,592,365,33,91,489,585,366,34,89,490,586,364,32,90,488,584,36,368,87,492,588,37,369,88,493,589,35,367,86,491,587,684,688,680,673,651,229,645,646,649,659,230,652,654,657,643,231,637,638,641,228,619,613,614,617,627,226,621,622,625,227,635,628,630,633,27,570,220,142,501,28,568,221,140,502,26,569,222,141,500,603,602,223,596,599,611,604,224,606,609,571,25,225,143,503,698,699,702,701,398,183,154,514,582,399,181,155,515,583,397,182,156,513,581,179,394,157,510,578,395,180,158,511,579,178,396,159,512,580,152,389,174,505,573,153,390,172,506,574,151,388,173,504,572,392,148,177,508,576,393,149,175,509,577,391,150,176,507,575,667,671,670,663,350,265,386,334,302,351,266,387,335,303,349,267,385,336,301,264,346,382,337,298,347,262,383,338,299,263,348,384,339,300,377,341,256,332,293,378,342,257,333,294,376,340,258,331,292,344,380,259,328,296,345,381,260,329,297,343,379,261,330,295,674,676,681,678 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#73fd82887325b6d09523ca7385118fdff4d39fe9410b39daf9f2816ebeaae0b3, 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 18:16:59 · history