Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 27b62634deb2…

magma 27b62634deb2
Size
381
Isomorphism class hash
27b62634deb2396fda2e9b00eae555d7b3f28ac65889113813d109bbc9ca0f7e
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 23:34:45
Display reorder
380,153,163,158,148,138,143,208,198,203,223,213,218,12,293,13,73,78,118,108,113,133,123,128,10,286,11,55,60,51,103,98,298,93,83,30,22,27,45,37,40,193,183,188,178,168,301,300,302,303,304,305,267,257,262,282,273,277,233,238,228,248,253,88,68,173,243,338,332,358,343,348,374,378,367,352,363,151,160,156,145,135,140,207,196,201,222,211,216,6,290,5,71,76,116,105,111,131,120,125,2,288,3,57,62,52,100,95,296,91,81,34,21,26,47,35,41,190,180,185,176,166,329,327,328,326,324,325,266,255,260,281,271,275,231,236,226,246,251,86,66,171,240,335,331,355,341,345,371,376,365,351,361,150,161,155,146,136,141,206,195,202,221,212,217,4,291,7,70,75,115,106,110,130,121,126,15,287,14,58,63,53,101,96,295,90,80,32,23,28,48,38,43,191,181,186,175,165,306,307,308,309,310,311,268,258,263,283,274,278,232,237,227,245,250,85,65,170,241,336,333,356,340,346,370,375,368,353,360,152,162,157,147,137,142,205,197,200,220,210,215,9,292,8,72,77,117,107,112,132,122,127,0,285,1,56,61,50,102,97,297,92,82,31,20,25,46,36,42,192,182,187,177,167,318,319,320,321,322,323,265,256,261,280,272,276,230,235,225,247,252,87,67,172,242,337,330,357,342,347,372,377,366,350,362,154,164,159,149,139,144,209,199,204,224,214,219,16,294,17,74,79,119,109,114,134,124,129,19,289,18,59,64,54,104,99,299,94,84,33,24,29,49,39,44,194,184,189,179,169,317,315,316,314,312,313,269,259,264,284,270,279,234,239,229,249,254,89,69,174,244,339,334,359,344,349,373,379,369,354,364 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#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {71} 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 23:34:46 · history