Equation 677 Database

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Magma c06eed93046e…

magma c06eed93046e
Size
321
Isomorphism class hash
c06eed93046e33d763846295b5fe88abf58c26c82a6c5cf5b4c9d437e319d081
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 22:49:53
Display reorder
300,22,146,153,44,105,23,42,144,154,106,145,43,21,155,107,18,149,152,40,108,147,19,150,41,109,20,148,151,39,110,13,229,230,50,103,14,233,234,48,104,237,12,238,49,102,26,16,158,46,99,24,17,156,47,100,25,15,157,45,101,302,305,313,316,240,265,264,266,267,241,270,269,268,271,272,274,242,273,275,243,260,261,262,263,252,244,253,254,255,245,256,257,258,259,246,289,288,291,290,247,293,292,295,294,296,248,297,299,298,284,249,285,286,287,277,250,276,278,279,281,251,280,282,283,317,319,318,320,120,5,178,207,219,121,208,3,179,220,4,209,122,177,221,119,0,181,206,218,2,117,182,204,216,118,1,180,205,217,111,11,176,213,225,112,9,174,214,226,10,113,175,215,227,7,114,172,212,224,8,115,173,210,222,6,116,171,211,223,311,309,303,304,86,188,195,138,126,84,139,186,196,127,187,140,85,197,128,82,191,194,137,125,189,83,192,135,123,81,190,193,136,124,77,231,201,228,132,75,235,202,232,133,239,76,203,236,134,184,80,200,143,131,185,78,198,141,129,183,79,199,142,130,301,314,307,315,91,169,55,28,63,92,29,170,56,64,168,27,90,54,65,87,165,51,31,66,166,88,52,32,67,89,167,53,30,68,97,160,61,34,69,98,161,62,35,70,159,96,60,33,71,163,93,57,37,72,164,94,58,38,73,162,95,59,36,74,306,312,310,308 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#b2f3cd20f8767e98b3e6e1e1383f90e37f2ce11df778eec5ffdbe92cabb78104, 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 22:49:53 · history