Equation 677 Database

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Magma 3cb9b07fdba3…

magma 3cb9b07fdba3
Size
381
Isomorphism class hash
3cb9b07fdba3b4e60ee6b39f90c79096023725372171563831ac7f2988d203b4
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 23:23:09
Display reorder
380,256,45,1,38,39,37,3,0,2,6,4,5,201,191,196,291,205,210,234,224,229,249,239,244,59,57,58,250,60,61,176,181,185,161,165,170,287,142,137,152,157,147,281,296,275,265,271,260,305,303,304,302,301,300,133,123,128,116,108,114,103,219,104,102,100,101,341,345,335,352,356,366,364,334,370,375,257,67,66,64,65,63,74,75,73,77,78,76,203,193,198,293,208,213,232,222,227,247,237,242,9,7,8,251,10,62,178,183,188,163,168,173,288,143,138,153,158,148,280,295,276,268,272,263,309,310,311,306,307,308,130,120,125,117,107,112,82,217,83,81,79,80,342,349,336,353,358,368,362,332,373,378,259,92,91,93,90,89,20,18,19,17,94,16,204,194,199,294,209,214,233,223,228,248,238,243,86,84,85,254,87,88,179,184,189,164,169,174,289,144,139,154,159,149,284,299,279,267,274,262,321,322,323,318,319,320,134,124,129,118,106,111,98,218,99,97,95,96,344,348,339,354,359,369,363,333,374,379,258,14,15,11,12,13,53,51,52,56,54,55,200,190,195,290,206,211,231,221,226,245,235,240,50,48,49,253,46,47,175,180,186,160,166,171,285,141,136,150,156,145,283,298,278,269,273,264,325,326,324,328,329,327,132,122,127,119,109,113,21,215,22,25,23,24,343,347,338,351,355,365,360,330,371,376,255,44,43,41,42,40,26,27,28,29,30,31,202,192,197,292,207,212,230,220,225,246,236,241,70,68,69,252,71,72,177,182,187,162,167,172,286,140,135,151,155,146,282,297,277,266,270,261,315,316,317,312,313,314,131,121,126,115,105,110,36,216,35,33,34,32,340,346,337,350,357,367,361,331,372,377 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, 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 23:23:10 · history