Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 432642090544…

magma 432642090544
Size
381
Isomorphism class hash
4326420905449075d0633cd65af677203b9ec9d44c462689a06b906498134199
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 23:36:08
Display reorder
380,259,254,264,269,274,279,209,214,219,194,199,204,79,84,74,17,294,16,169,174,164,184,189,179,144,134,139,159,149,154,313,311,312,316,314,315,69,59,64,54,49,289,19,299,18,93,99,88,44,33,39,284,24,29,221,226,234,239,244,249,119,124,129,104,109,114,359,349,334,339,364,354,344,374,379,369,257,252,263,268,273,278,208,213,218,193,198,203,78,83,73,13,293,12,168,173,163,183,188,178,143,133,138,158,148,153,308,309,310,306,329,307,68,58,63,53,48,288,15,298,14,90,98,85,43,32,38,283,23,28,224,229,233,238,243,248,118,123,128,103,108,113,358,348,333,338,362,353,343,373,378,368,256,251,260,266,271,276,206,211,216,190,196,201,75,82,70,9,292,8,166,172,162,182,186,176,142,132,137,157,147,152,326,327,328,323,324,325,66,55,62,52,47,287,11,297,10,94,97,89,40,31,35,282,22,27,220,225,230,235,240,245,117,122,127,102,107,112,356,347,331,337,363,352,342,372,377,366,258,253,261,265,270,275,205,210,215,191,195,200,76,80,72,4,290,3,165,170,161,180,185,175,141,131,136,155,145,150,302,301,300,305,303,304,65,56,61,50,45,286,7,295,6,92,95,87,41,34,36,281,20,25,222,227,231,236,241,246,115,120,125,101,106,111,355,345,330,336,360,350,341,370,375,365,255,250,262,267,272,277,207,212,217,192,197,202,77,81,71,2,291,5,167,171,160,181,187,177,140,130,135,156,146,151,322,320,321,319,317,318,67,57,60,51,46,285,0,296,1,91,96,86,42,30,37,280,21,26,223,228,232,237,242,247,116,121,126,100,105,110,357,346,332,335,361,351,340,371,376,367 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {74} 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 23:36:09 · history