Equation 677 Database

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Magma 3cc824f7ae99…

magma 3cc824f7ae99
Size
321
Isomorphism class hash
3cc824f7ae99774250b913b71ae4bee1b00ec6d897dae2dfca52779205e669a5
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 22:27:12
Display reorder
300,79,125,85,141,29,80,27,123,86,142,124,28,78,84,143,25,82,121,88,140,26,83,122,89,138,24,81,120,87,139,77,131,35,91,132,75,129,33,92,133,76,130,34,90,134,127,73,31,94,135,128,74,32,95,136,126,72,30,93,137,315,316,307,305,12,257,259,258,256,13,263,260,262,261,252,255,14,254,253,271,15,269,270,268,275,16,273,274,272,267,17,265,266,264,18,280,283,282,281,19,285,287,286,284,20,276,279,278,277,292,21,295,294,293,297,22,299,298,296,288,23,291,290,289,319,320,317,318,51,109,157,176,107,52,105,110,158,174,108,106,53,156,175,103,50,112,160,179,104,48,113,161,177,102,49,111,159,178,57,115,98,163,171,58,116,96,164,172,59,114,97,162,173,118,56,101,166,170,119,54,99,167,168,117,55,100,165,169,308,304,303,301,65,230,231,145,1,63,0,233,232,146,228,2,64,229,144,3,61,237,236,148,4,62,238,239,149,5,60,235,234,147,71,243,6,242,151,69,245,7,244,152,70,240,8,241,150,248,67,9,249,154,251,68,10,250,155,246,66,11,247,153,312,313,311,314,41,217,192,187,215,39,213,218,193,188,216,214,40,194,186,211,37,220,195,190,212,38,221,196,191,210,36,219,197,189,47,223,206,198,185,45,224,204,199,183,46,222,205,200,184,226,43,209,201,181,227,44,207,202,182,225,42,208,203,180,309,306,310,302 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#34588157c307db5531c4fa8d738de6f4f43dd6ced943a299dd02fbb5d9b36bf1, 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 22:27:13 · history