Equation 677 Database

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Magma 17eb9893e0ba…

magma 17eb9893e0ba
Size
511
Isomorphism class hash
17eb9893e0ba9a1d04c447b144e6f192f6ea8cb270fc18c166c93a7775ed8268
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 460 (nullity 51) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 22:16:37
Display reorder
218,224,222,217,220,219,221,216,510,225,223,420,20,226,427,229,188,195,439,245,488,187,426,228,191,434,423,428,418,189,463,441,248,214,424,465,190,437,501,506,503,508,502,498,500,499,505,416,487,209,491,413,493,201,204,198,210,417,495,211,206,199,415,490,202,212,422,497,246,509,208,203,414,492,200,496,194,486,464,494,193,205,421,213,440,207,507,419,196,232,2,3,197,6,19,22,489,215,431,425,462,435,430,429,433,436,432,1,438,192,504,230,63,405,299,305,134,102,264,235,483,26,383,247,42,281,393,404,293,59,452,275,397,150,341,455,84,363,257,457,323,347,337,387,258,379,390,309,474,87,98,252,108,180,91,116,14,268,162,138,119,146,285,112,73,130,265,32,289,479,55,177,359,165,158,154,4,472,461,31,94,126,327,38,375,142,122,319,39,315,21,80,169,90,9,173,477,49,351,371,450,312,316,401,367,240,344,181,355,67,333,374,93,308,336,346,141,133,378,234,471,115,288,277,89,304,292,271,332,58,444,233,301,176,350,443,101,260,263,460,236,408,354,403,254,392,280,326,485,69,10,340,172,45,41,125,13,314,179,34,86,72,284,129,111,145,322,28,318,482,79,118,366,54,62,168,149,468,449,37,137,157,358,153,400,161,184,362,97,256,51,121,66,30,8,76,484,7,382,298,446,295,267,343,386,239,311,83,370,107,396,278,46,302,310,282,99,61,243,391,480,174,238,364,15,296,384,338,255,123,447,342,334,185,388,454,182,313,250,451,356,306,300,372,249,352,330,406,469,120,131,398,170,113,103,163,151,241,147,88,47,35,348,74,85,60,380,23,272,473,70,143,324,105,12,127,52,467,458,24,64,95,287,17,409,135,81,290,155,269,139,56,159,43,166,109,476,117,320,261,445,345,328,368,360,376,273,77,286,29,394,335,124,244,262,297,128,100,361,399,470,11,253,303,92,321,227,231,385,33,442,291,365,167,279,453,132,276,402,456,373,283,270,329,331,407,274,357,466,152,148,237,75,5,82,53,164,317,104,50,114,186,259,44,36,156,266,106,349,478,96,171,353,48,27,183,110,481,448,178,25,68,325,136,412,144,57,251,40,242,78,71,0,16,175,140,475,65,294,410,459,377,307,395,369,389,339,18,381,160,411 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 511 = 11 + 5*100, 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#7203802ce09cb3ec8d6de67c66baaaee48b8f9740ddbb4ddbea7cfe0a09d6dc5, M = {0, 6, 8, 12, 17, 23, 27, 29, 33, 44, 86} 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, 100): MacNeish's product over GF(4) x GF(25); GF(4) = F_2[x]/(x^2 + x + 1), GF(25) = F_5[x]/(x^2 + 2); 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: 511.

last edited by qawbecrdtey at 2026-10-06 22:16:38 · history