Equation 677 Database

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Magma 4d5118d5118d…

magma 4d5118d5118d
Size
321
Isomorphism class hash
4d5118d5118da5e863912056ec9bc09b8f4d7a897870082438f86a9072629eef
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 22:46:00
Display reorder
315,241,251,275,265,60,164,92,223,61,165,91,222,63,93,163,220,62,94,162,221,242,252,264,274,90,216,66,157,88,217,64,158,89,215,65,159,219,87,68,160,250,273,243,263,86,218,67,161,44,45,46,47,48,49,50,51,283,281,282,280,305,300,308,311,293,276,295,291,181,153,4,214,180,152,1,213,183,2,155,210,184,3,156,211,182,0,154,212,9,206,179,151,277,294,292,290,8,205,178,150,208,5,176,148,6,209,177,149,7,207,175,147,116,117,115,119,120,118,122,123,124,125,126,121,310,306,303,312,140,71,168,129,141,130,72,169,261,258,245,267,138,70,128,167,260,244,257,266,139,69,127,166,75,172,145,133,76,173,146,134,77,174,144,135,268,246,262,259,73,170,142,131,74,171,143,132,31,32,30,34,35,33,136,137,288,286,287,289,302,319,301,313,279,285,284,278,38,22,83,52,39,23,82,53,235,249,232,238,37,85,24,54,36,84,25,55,81,56,43,26,248,239,237,233,80,57,42,27,58,78,40,28,79,59,41,29,247,240,236,234,18,16,17,21,19,20,13,14,11,12,10,15,309,304,307,314,197,96,191,108,195,109,97,189,196,110,95,190,200,99,107,194,198,100,105,192,199,98,106,193,253,269,272,255,254,270,271,256,101,188,201,114,187,103,204,113,104,185,202,111,102,186,203,112,224,225,226,227,228,229,230,231,298,296,297,299,317,316,318,320 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 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#a08efb2611f2171bf6f734a20baed2f33f3141d650739b05e30e32bcbe11c9bc, M = {60} 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 2026-10-01 22:46:01 · history