Equation 677 Database

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Magma f4271f579c26…

magma f4271f579c26
Size
381
Isomorphism class hash
f4271f579c26d674d3a750286f0c681e7da54f02232a8aa0ed71f58e806caa95
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 23:49:10
Display reorder
380,36,35,37,32,33,34,318,319,320,321,322,317,227,232,237,242,247,222,82,87,92,67,72,77,172,147,152,157,162,167,292,142,127,132,137,282,28,29,30,31,26,27,267,272,277,252,257,262,217,38,287,297,207,212,197,177,182,192,187,202,97,102,107,112,117,122,352,342,360,356,369,330,334,346,375,371,62,60,52,54,56,58,308,309,310,305,306,307,229,234,239,244,249,224,83,88,93,68,73,78,173,148,154,158,163,168,294,144,129,134,139,284,46,48,50,40,42,44,269,274,279,254,259,264,219,64,289,299,209,214,199,179,184,194,189,204,98,103,108,113,118,123,354,333,364,357,367,343,337,347,378,374,21,20,22,23,24,19,325,326,327,328,323,324,226,231,236,241,246,220,81,86,91,65,70,76,170,146,151,156,161,165,291,140,126,130,135,281,13,14,15,16,17,18,265,271,275,250,255,260,215,1,285,295,205,210,196,176,181,191,186,200,96,101,105,110,115,120,351,336,362,359,366,335,341,349,376,372,61,59,51,53,55,57,329,304,300,302,303,301,228,233,238,243,248,223,84,89,94,69,74,79,174,149,153,159,164,169,293,143,128,133,138,283,45,47,49,39,41,43,268,273,278,253,258,263,218,63,288,298,208,213,198,178,183,193,188,203,99,104,109,114,119,124,353,339,363,355,365,344,338,348,377,373,7,12,8,9,10,11,316,311,312,313,314,315,225,230,235,240,245,221,80,85,90,66,71,75,171,145,150,155,160,166,290,141,125,131,136,280,5,6,0,2,3,4,266,270,276,251,256,261,216,25,286,296,206,211,195,175,180,190,185,201,95,100,106,111,116,121,350,331,361,358,368,332,340,345,379,370 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#e7d843eeb4140ee4f2ae7f87ad1590cd2b2e584cf01474530a75f9f611790378, M = {75} 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 23:49:11 · history