Equation 677 Database

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Magma fe98c67b3170…

magma fe98c67b3170
Size
381
Isomorphism class hash
fe98c67b3170fd1a762c7a10379bdb9df6b9f33d13471368d4ef4792584966dc
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 23:28:04
Display reorder
380,247,197,297,42,97,147,5,57,107,157,207,257,306,307,308,309,310,311,72,122,22,222,272,172,2,52,102,152,202,252,87,137,37,237,287,187,167,217,267,17,62,117,177,277,227,127,27,82,262,212,162,67,112,12,77,132,32,282,232,182,192,292,242,142,47,92,342,347,357,337,352,367,372,332,362,377,246,196,296,40,96,145,6,55,106,155,206,256,301,300,302,303,304,305,70,121,21,221,271,170,0,51,101,150,200,250,85,135,36,236,286,186,165,216,266,16,61,115,176,276,226,125,26,80,261,211,161,65,110,11,76,130,31,281,231,180,190,290,240,141,45,91,341,346,356,336,351,366,370,330,361,376,248,198,298,43,98,148,7,58,108,158,208,258,315,316,317,312,313,314,73,123,23,223,273,173,3,53,103,153,203,253,88,138,38,238,288,188,168,218,268,18,63,118,178,278,228,128,28,83,263,213,163,68,113,13,78,133,33,283,233,183,193,293,243,143,48,93,343,348,359,338,353,368,373,333,363,378,249,199,299,44,99,149,8,59,109,159,209,259,329,327,328,326,324,325,74,124,24,224,274,174,4,54,104,154,204,254,89,139,39,239,289,189,169,219,269,19,64,119,179,279,229,129,29,84,264,214,164,69,114,14,79,134,34,284,234,184,194,294,244,144,49,94,344,349,358,339,354,369,374,334,364,379,245,195,295,41,95,146,9,56,105,156,205,255,323,321,322,320,318,319,71,120,20,220,270,171,1,50,100,151,201,251,86,136,35,235,285,185,166,215,265,15,60,116,175,275,225,126,25,81,260,210,160,66,111,10,75,131,30,280,230,181,191,291,241,140,46,90,340,345,355,335,350,365,371,331,360,375 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#564914c332df918b1bab25ab6758cc0c591864f3f64c8c0ef251305010e22f83, M = {72} 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 23:28:06 · history