Equation 677 Database

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Magma 382c3bdab07b…

magma 382c3bdab07b
Size
321
Isomorphism class hash
382c3bdab07ba368d03d9d7d1d0a7694efbeb4434181b893d77194ad8f3da8ca
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 22:32:31
Display reorder
300,50,226,116,24,98,224,96,48,114,25,97,225,49,115,26,53,229,101,119,27,51,227,99,117,28,52,228,100,118,29,56,232,104,111,30,54,230,102,112,31,55,231,103,113,32,235,59,107,110,33,108,233,57,105,34,234,58,106,109,35,311,303,305,302,44,261,263,262,260,252,255,42,254,253,259,256,43,258,257,47,272,275,274,273,45,265,267,266,264,46,268,271,270,269,39,284,287,286,285,40,276,279,278,277,41,280,283,282,281,297,38,299,298,296,290,289,36,291,288,293,37,295,294,292,320,317,318,319,19,181,136,154,218,179,216,20,134,152,217,180,18,135,153,22,177,221,139,157,23,178,219,137,155,21,176,220,138,156,17,236,238,131,160,15,182,222,132,158,16,183,223,133,159,248,13,251,130,163,128,241,14,243,161,244,12,247,129,162,314,315,307,304,75,166,62,142,1,164,0,76,60,140,2,165,77,61,141,74,169,3,65,145,72,167,4,63,143,73,168,5,64,144,81,172,6,68,148,82,170,7,66,146,83,171,8,67,147,175,80,9,71,151,69,173,78,10,149,174,79,11,70,150,309,312,306,301,88,125,189,206,193,126,194,89,190,204,192,127,87,191,205,84,124,196,188,209,85,122,197,186,207,86,123,195,187,208,94,239,199,237,212,95,120,200,184,210,93,121,198,185,211,249,90,202,250,215,242,240,91,203,213,245,92,201,246,214,316,308,310,313 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#57f0a2716884c2711bcb20a2573985b973a13e807353fc83680d5538f9af708e, 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 22:32:32 · history