Equation 677 Database

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Magma 746e2f3a1da4…

magma 746e2f3a1da4
Size
321
Isomorphism class hash
746e2f3a1da4347f4174c982eb163c48779a64b0bc3bf9a30a0fea56534f25ea
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 22:55:24
Display reorder
300,3,236,186,238,199,4,229,187,230,197,5,233,185,234,198,220,2,182,222,195,224,1,183,226,196,217,0,184,218,194,177,116,119,9,190,178,117,120,10,188,176,115,118,11,189,213,180,214,8,193,113,181,122,6,191,114,179,121,7,192,303,308,313,316,241,299,298,296,297,242,290,291,289,288,240,294,295,292,293,283,244,282,280,281,287,245,286,284,285,279,243,278,277,276,262,263,260,247,261,254,255,252,248,253,258,259,256,246,257,275,274,272,250,273,267,266,265,251,264,271,270,269,249,268,319,318,320,317,14,175,46,211,59,12,173,47,209,57,13,174,45,210,58,171,17,42,207,55,172,15,43,208,56,170,16,44,206,54,37,166,202,20,50,38,164,200,18,48,36,165,201,19,49,169,40,205,23,53,167,41,203,21,51,168,39,204,22,52,302,301,306,311,91,32,139,239,237,92,30,137,231,228,90,31,138,235,232,35,94,135,223,221,33,95,136,227,225,34,93,134,219,216,130,27,127,89,110,128,28,125,87,108,129,29,126,88,109,26,133,215,85,212,24,131,124,86,111,25,132,123,84,112,304,314,309,315,66,106,150,82,163,67,107,151,83,161,68,105,149,81,162,102,69,146,78,159,103,70,147,79,160,104,71,148,80,158,141,97,73,64,154,142,98,74,65,152,140,96,72,63,153,100,144,76,60,157,101,145,77,61,155,99,143,75,62,156,310,305,312,307 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#cb899e6f30effddffe30366e2e9dc963aa0ce854a3a9ff04422e3e195000d2a8, 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 22:55:25 · history