Equation 677 Database

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Magma eb757e603414…

magma eb757e603414
Size
595
Isomorphism class hash
eb757e603414e26de86e79b1efbfb58a9280b7a39a8ac1dc5b5328ea65c99727
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 10:42:49
Display reorder
131,130,132,133,134,135,56,55,57,58,59,54,64,63,65,60,61,62,310,312,311,308,309,449,443,442,444,445,446,447,543,521,590,566,563,182,186,152,183,184,185,167,101,99,100,103,102,67,72,68,69,70,71,4,3,5,187,188,153,177,176,175,150,1,2,81,80,82,83,84,222,171,235,236,237,238,172,205,204,206,159,202,203,503,502,501,506,504,505,398,455,397,399,400,401,351,350,349,353,354,352,381,380,379,383,384,382,489,491,490,488,487,486,405,407,406,404,402,403,461,456,457,272,270,271,410,409,408,411,412,413,549,551,514,528,510,529,535,537,555,558,571,576,567,559,587,554,41,40,36,37,38,39,29,26,24,25,28,27,53,52,48,49,50,51,110,109,111,112,107,108,115,114,116,117,118,113,120,119,121,122,123,234,199,158,200,201,198,157,189,193,154,190,191,192,303,302,304,306,307,305,290,289,288,285,286,287,509,508,507,498,499,500,497,496,495,493,494,492,332,331,333,334,335,336,345,344,343,347,348,346,266,265,264,268,269,267,330,329,328,325,326,327,530,531,542,548,550,511,541,540,579,593,585,584,589,570,557,591,93,92,94,89,90,91,7,10,8,9,6,11,45,44,46,47,42,43,30,35,31,32,33,34,78,77,73,74,75,76,146,145,147,148,149,257,255,246,250,249,248,229,254,253,247,251,256,252,451,450,459,453,454,452,418,460,417,414,415,416,363,362,361,365,366,364,424,423,422,420,421,419,426,425,427,428,429,430,375,374,373,377,378,376,318,317,316,314,315,313,283,282,284,281,279,280,534,515,532,524,525,536,539,538,560,568,594,575,562,582,578,581,124,129,125,126,127,128,66,213,211,212,162,214,233,170,230,169,231,232,245,244,174,142,143,144,96,95,97,98,225,226,156,195,196,197,155,194,164,217,218,215,216,163,242,241,243,173,239,240,472,482,481,471,479,480,324,323,322,319,320,321,299,301,300,298,296,297,337,339,338,342,340,341,463,462,464,465,466,485,368,367,369,370,371,372,292,448,291,294,295,293,439,441,440,437,438,436,544,547,527,517,522,523,518,520,592,574,556,583,580,588,572,586,22,21,23,18,19,20,0,179,178,151,181,180,207,160,208,209,161,210,228,227,168,105,106,104,86,85,87,88,223,224,220,219,165,221,166,79,136,141,137,138,139,140,17,16,12,13,14,15,263,262,261,260,259,258,359,358,360,357,355,356,483,484,469,475,476,474,477,470,478,468,467,473,392,391,393,394,395,396,277,276,278,273,274,275,435,458,434,432,433,431,390,389,388,385,386,387,516,519,512,546,545,526,513,533,577,573,569,553,564,565,552,561 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = the submagma generated by {30, 42} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 10:42:53 · history