Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 1d3833a7e6ff…

magma 1d3833a7e6ff
Size
381
Isomorphism class hash
1d3833a7e6ff09d93d410a031231f1b00d90571e32f14410d8a88c80d8df93c3
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 23:34:12
Display reorder
380,32,26,53,19,39,46,11,4,12,326,329,33,27,48,20,40,47,6,5,13,318,34,28,49,21,41,42,7,1,14,321,35,29,50,22,36,43,8,0,15,30,322,24,51,23,37,44,9,2,16,25,324,31,52,18,38,45,10,3,17,59,55,56,57,58,54,331,349,330,332,376,344,350,347,366,348,159,124,145,117,137,138,103,131,110,316,303,160,125,146,118,132,139,104,126,111,302,161,120,147,119,133,140,105,127,112,311,156,121,148,114,134,141,106,128,113,157,312,122,149,115,135,142,107,129,108,123,314,158,144,116,136,143,102,130,109,151,153,154,155,150,152,355,354,352,357,371,358,356,336,372,353,241,278,233,270,248,226,260,255,268,325,327,242,279,228,271,249,227,261,256,269,328,243,280,229,272,250,222,262,257,264,319,244,281,230,273,251,223,263,252,265,245,320,276,231,274,246,224,258,253,266,277,323,240,232,275,247,225,259,254,267,239,235,236,237,238,234,377,345,335,333,334,351,369,367,368,370,294,72,284,100,61,68,86,79,93,317,301,295,73,285,101,62,69,87,80,94,300,296,74,286,96,63,70,88,81,95,310,297,75,287,97,64,71,89,82,90,298,313,76,282,98,65,66,84,83,91,77,315,299,283,99,60,67,85,78,92,293,289,290,291,292,288,346,337,359,374,373,361,378,339,360,338,197,191,212,184,198,205,170,163,177,305,306,192,186,213,185,199,206,171,164,178,307,193,187,214,180,200,207,172,165,179,308,194,188,215,181,201,208,173,166,174,195,309,189,210,182,202,209,168,167,175,190,304,196,211,183,203,204,169,162,176,218,220,221,216,217,219,363,341,362,379,375,343,342,364,365,340 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#884b08d51449ed77e1a667f669d83886c6bad5f585ed6ff76e2bf63ff2c61f44, 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 23:34:13 · history