Equation 677 Database

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Magma 4bb39fe85002…

magma 4bb39fe85002
Size
321
Isomorphism class hash
4bb39fe85002a4166715baf36680dd646fc6d629359f87f7036506adbef62759
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 22:50:09
Display reorder
300,26,112,88,200,184,24,113,89,198,185,25,111,87,199,183,108,29,84,203,180,109,27,85,201,181,110,28,86,202,182,32,118,94,195,190,30,119,95,196,191,31,117,93,197,189,114,35,90,194,186,115,33,91,192,187,116,34,92,193,188,306,309,307,305,251,269,268,271,270,249,272,273,275,274,250,265,264,266,267,252,247,253,255,254,256,248,257,259,258,260,246,261,262,263,242,292,293,295,294,240,297,296,298,299,241,288,289,290,291,276,245,277,279,278,281,243,280,283,282,285,244,284,287,286,317,319,320,318,3,208,15,225,224,4,209,16,226,227,5,207,17,223,222,204,2,14,216,217,205,1,12,218,219,206,0,13,220,221,9,214,21,236,237,10,215,22,238,239,11,213,23,235,234,210,8,20,229,228,211,6,18,230,231,212,7,19,232,233,311,312,313,314,129,51,69,99,41,130,52,70,100,39,131,53,71,101,40,50,128,68,98,37,48,126,66,96,38,49,127,67,97,36,120,57,60,105,47,121,58,61,106,45,122,59,62,107,46,56,123,63,104,43,54,124,64,102,44,55,125,65,103,42,301,302,303,310,72,170,142,146,166,73,168,143,144,167,74,169,141,145,165,173,75,138,149,162,171,76,139,147,163,172,77,140,148,164,78,176,133,152,157,79,174,134,150,158,80,175,132,151,156,179,81,136,155,160,177,82,137,153,161,178,83,135,154,159,308,315,316,304 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#b3dac6ff36f26cacc8049b7c1e09fd794a0277a3d237510b4c6377f158398334, 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 22:50:10 · history