Equation 677 Database

← all  ·  ← by size  ·  ← size 336

Magma ba39926590b0…

magma ba39926590b0
Size
336
Isomorphism class hash
ba39926590b0b6ed03200844a920176a5a8967ac319b45774cb02ec708075aaf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 335) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 08:52:16
Display reorder
112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,319,286,262,281,277,203,49,176,204,50,177,205,51,178,206,52,179,207,53,180,208,259,278,287,260,181,197,43,182,198,44,183,199,45,184,200,46,185,201,47,202,279,261,285,280,48,8,0,1,2,3,4,5,6,7,9,10,293,294,291,292,318,316,325,334,309,296,299,300,107,54,72,108,55,73,109,56,74,110,57,75,111,58,76,100,59,77,101,60,78,102,61,67,307,297,298,308,62,68,103,63,69,104,64,105,70,65,106,71,66,209,212,213,214,215,216,217,218,219,230,232,234,210,211,229,322,332,329,321,13,29,136,137,14,30,138,11,254,268,247,255,127,15,31,128,248,252,266,249,21,129,16,22,130,17,23,131,18,24,132,19,25,133,20,26,267,250,253,251,134,27,12,135,28,98,90,91,92,93,94,95,96,97,99,89,303,304,305,306,324,333,323,330,295,310,301,302,36,186,80,37,187,81,38,188,263,257,282,264,39,189,82,40,190,83,41,191,84,42,192,85,258,283,265,256,193,86,32,194,87,33,195,34,88,196,35,79,284,290,288,289,221,222,223,224,225,226,228,231,233,235,220,227,315,327,331,317,173,154,145,146,174,155,147,175,156,148,164,157,149,165,158,150,166,159,139,167,160,140,168,161,269,274,272,270,275,273,271,276,162,141,169,163,142,170,151,171,143,152,172,144,153,237,238,239,240,241,242,243,244,245,246,236,313,314,312,311,320,326,328,335 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 336 = 16 + 5*64, 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#9ec34e5d7233e8953a2fa801c206b195473c59d0c7836b1f0f582edb83284699, M = {0, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 44, 48, 54, 58, 77} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-08 08:52:17 · history