Equation 677 Database

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Magma c5e2f63a86e0…

magma c5e2f63a86e0
Size
321
Isomorphism class hash
c5e2f63a86e0161ba8b8e473340a937cd22417f4b87093c75e0468bd8b04c828
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 22:49:56
Display reorder
300,83,98,76,62,42,81,99,43,77,60,82,97,44,75,61,86,101,45,79,65,84,102,46,80,63,85,100,47,78,64,89,96,40,74,68,87,94,41,72,66,73,88,95,39,67,247,246,36,245,244,93,90,37,71,69,92,91,38,1,70,312,315,316,310,262,263,260,261,25,254,255,26,252,253,258,259,24,256,257,274,275,28,273,272,266,267,29,264,265,270,271,27,268,269,286,287,31,285,284,278,279,32,276,277,281,282,283,30,280,299,298,34,297,296,291,290,35,288,289,295,294,33,293,292,318,319,320,317,152,128,148,109,55,150,126,56,149,110,151,127,54,147,111,155,131,58,144,112,153,129,59,145,113,154,130,57,146,114,158,134,53,139,107,156,132,51,140,108,138,157,133,52,106,137,161,49,142,103,135,159,50,143,104,136,160,48,141,105,302,301,303,304,10,164,117,187,14,11,162,12,115,185,9,163,13,116,186,6,167,17,120,190,7,165,15,118,188,8,166,16,119,189,4,170,20,123,193,2,168,18,121,191,122,3,169,19,192,251,250,23,248,249,171,5,21,124,194,172,0,22,125,195,311,314,313,309,224,210,225,199,176,220,208,177,221,200,222,209,178,223,201,230,213,175,231,198,227,211,173,226,196,229,212,174,228,197,236,216,182,237,205,233,214,183,232,206,235,234,215,184,207,219,242,181,243,204,217,239,179,238,202,218,240,180,241,203,307,305,306,308 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#b307f9e79abd0b0dc3c5454ee1dbc0a12bcd3b395b4c4aa55143605b1deda3bc, 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 22:50:02 · history