Equation 677 Database

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Magma 947c8ebc6e66…

magma 947c8ebc6e66
Size
381
Isomorphism class hash
947c8ebc6e66305369b6d6e2de97f32b86b3c2d515db7b52131633ec8f5664f9
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:20:14
Display reorder
380,116,103,112,306,99,107,98,90,94,108,114,104,113,304,100,105,96,91,109,95,115,102,111,305,101,106,97,92,110,93,73,87,82,64,60,309,78,86,77,69,70,88,74,83,65,61,307,79,84,75,71,89,72,81,63,62,308,80,85,76,67,68,118,119,117,66,343,363,365,362,342,344,364,375,369,371,268,253,262,300,297,257,293,279,286,258,267,254,263,301,298,255,291,280,259,287,269,252,261,329,299,256,292,281,260,285,284,240,247,266,244,303,294,251,289,276,277,241,282,248,264,245,315,295,249,290,278,242,283,246,265,243,302,296,250,288,270,271,273,274,275,272,357,360,358,356,359,370,341,340,355,361,32,50,59,327,46,51,42,37,41,55,30,48,57,328,47,52,43,38,56,39,31,49,58,326,45,53,44,36,54,40,20,3,29,11,7,324,25,2,21,16,17,4,18,27,9,8,325,26,1,22,15,5,19,28,10,6,323,24,0,23,14,12,34,35,33,13,334,376,373,345,366,346,372,368,367,374,197,235,193,313,183,188,182,202,206,189,195,236,194,314,184,186,180,203,190,204,196,234,192,316,185,187,181,201,191,205,227,210,239,218,214,310,232,209,228,223,224,211,225,237,216,215,311,233,207,229,222,212,226,238,217,213,312,231,208,230,221,219,199,200,198,220,331,338,377,378,339,332,353,379,354,333,177,167,176,319,166,174,162,157,158,123,178,168,120,317,164,175,163,155,124,159,179,169,121,318,165,173,161,156,122,160,140,126,149,131,130,322,148,171,144,139,137,127,141,150,132,128,320,146,172,145,138,125,142,151,133,129,321,147,170,143,134,135,154,152,153,136,351,347,350,352,336,349,330,337,348,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#1d02f36e6e79c4e0d5c5938f4a162287d3bad833584e12b2db918f3e2fd08f81, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:20:15 · history