Equation 677 Database

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Magma 4cba8749c7c8…

magma 4cba8749c7c8
Size
321
Isomorphism class hash
4cba8749c7c87b8d06b2eaabddc92118fe179f5108489b3e736f6346034fd623
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 22:21:42
Display reorder
313,275,268,233,256,6,184,125,223,222,183,5,124,220,179,7,122,221,180,8,123,274,267,234,255,4,118,177,216,2,119,178,217,3,117,176,215,121,0,174,219,254,232,266,273,120,1,175,218,107,105,106,103,104,102,101,100,282,283,281,280,307,308,300,315,285,276,287,294,167,13,205,116,115,9,168,206,114,11,204,209,108,12,165,207,134,10,166,208,172,211,18,110,288,295,277,284,173,210,17,109,214,171,14,112,212,169,15,113,213,170,16,111,59,60,61,58,56,57,53,54,55,51,203,52,310,305,302,318,84,76,68,37,67,75,38,85,252,249,246,241,86,78,70,40,253,250,247,242,87,77,69,39,64,36,202,82,65,34,73,83,66,35,74,81,240,245,248,251,33,62,72,79,32,63,71,80,195,196,194,198,199,197,200,201,291,292,293,290,301,319,304,317,289,279,286,278,126,181,25,186,187,31,127,26,270,269,257,237,188,185,128,24,189,182,129,23,130,20,30,190,258,235,239,271,131,19,29,191,22,132,27,192,21,133,28,193,236,259,238,272,95,96,94,98,99,97,93,91,88,89,90,92,309,303,306,314,150,160,144,45,142,158,46,151,149,159,143,47,153,156,140,48,154,157,141,49,152,155,139,50,261,243,265,263,260,244,264,262,135,44,164,148,41,138,162,146,42,136,163,147,43,137,161,145,224,225,226,227,228,229,230,231,298,296,297,299,312,316,311,320 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#14697465b8cd7575930ebcd6f1cfb0d098649f4474b7abfd50cfc1485faac906, 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 22:21:43 · history