Equation 677 Database

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Magma 976126b0a405…

magma 976126b0a405
Size
321
Isomorphism class hash
976126b0a40542266a86785295ce1d069272a03738c985619181b7e6a2c724bb
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 22:21:11
Display reorder
300,126,30,141,107,38,142,127,105,31,36,143,32,128,106,37,140,129,103,29,41,138,130,104,27,39,139,131,102,28,40,147,132,113,240,241,148,133,111,244,245,149,134,112,248,249,146,135,109,35,24,144,136,110,33,25,145,137,108,34,26,313,314,304,309,265,266,264,18,267,269,268,19,270,271,273,274,272,20,275,261,260,21,262,263,253,252,22,254,255,257,256,23,258,259,289,288,16,291,290,292,293,17,295,294,296,297,15,299,298,284,285,12,286,287,276,277,13,278,279,280,281,14,282,283,319,317,318,320,54,44,69,9,189,70,55,10,42,190,71,43,56,11,191,68,57,8,47,188,66,58,6,45,186,67,59,7,46,187,75,60,1,50,195,76,61,0,48,196,77,62,2,49,197,74,63,3,53,194,72,64,4,51,192,73,65,5,52,193,305,308,301,302,236,230,201,79,214,202,234,80,228,215,203,229,235,78,213,200,232,82,226,217,198,233,83,227,218,199,231,81,225,216,207,243,85,221,242,208,247,86,219,246,209,251,84,220,250,206,238,88,224,211,204,239,89,222,212,205,237,87,223,210,312,316,311,315,173,158,177,91,117,178,171,92,156,118,179,157,172,90,119,176,169,94,161,116,174,170,95,159,114,175,168,93,160,115,183,164,97,153,123,184,162,98,154,124,185,163,96,155,125,182,167,100,152,122,180,165,101,150,120,181,166,99,151,121,310,303,307,306 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#0898d182914656a7d8331eed416fb390a2b0882bf44ec0102530c706a89c62d3, 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 22:21:12 · history