Equation 677 Database

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Magma b530ec05bcfb…

magma b530ec05bcfb
Size
381
Isomorphism class hash
b530ec05bcfbbf3cb0e2e32f7475acdfb4b5a6b68d70b96e99d3d34e4458b60e
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 23:16:14
Display reorder
380,139,149,144,134,124,129,30,31,210,27,28,29,164,154,159,179,169,174,84,89,94,74,254,79,312,313,314,315,316,317,104,108,99,294,119,114,259,264,268,274,279,289,180,186,191,196,201,206,226,231,236,241,245,296,19,18,16,15,17,215,221,6,5,280,4,3,356,346,331,340,335,369,354,374,364,379,135,145,140,131,121,126,46,47,213,25,26,48,161,151,156,175,165,170,81,87,91,71,251,77,308,306,307,311,309,310,101,106,96,290,115,110,255,260,265,271,276,286,183,188,193,198,203,208,227,232,237,242,247,297,52,51,53,49,50,218,223,55,54,283,56,57,357,348,333,343,338,365,350,371,360,376,138,148,143,133,123,128,58,59,214,1,0,60,163,153,158,178,168,173,83,88,93,73,253,78,318,319,320,321,322,323,103,107,98,293,118,113,258,263,267,273,278,288,184,189,194,199,204,209,229,234,239,244,249,299,64,63,65,61,62,219,224,67,66,284,68,69,359,349,334,344,339,368,353,373,363,378,136,146,141,130,120,125,32,10,211,9,7,8,160,150,155,176,166,171,82,86,92,70,252,76,326,327,328,324,329,325,100,105,95,291,116,111,256,261,269,270,275,285,181,185,190,195,200,205,225,230,235,240,246,295,11,12,13,14,20,216,220,24,23,281,22,21,355,345,330,341,336,366,351,370,361,375,137,147,142,132,122,127,37,36,212,35,33,34,162,152,157,177,167,172,80,85,90,72,250,75,303,304,305,301,300,302,102,109,97,292,117,112,257,262,266,272,277,287,182,187,192,197,202,207,228,233,238,243,248,298,45,2,40,39,38,217,222,42,41,282,43,44,358,347,332,342,337,367,352,372,362,377 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, M = {73} 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 23:16:15 · history