Equation 677 Database

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Magma 3eeb133635fd…

magma 3eeb133635fd
Size
321
Isomorphism class hash
3eeb133635fdbc238ef390af63bbc4840c39a0ca63ad25c72d5703601e007a44
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 22:21:04
Display reorder
300,104,51,61,172,77,62,105,173,78,52,63,50,103,171,79,102,60,53,227,231,199,59,54,169,242,244,213,212,170,80,12,56,165,97,81,13,57,166,98,82,14,55,164,96,83,58,11,167,100,84,229,230,168,101,85,99,239,240,226,217,301,306,315,302,280,282,178,281,283,179,284,285,287,286,177,278,277,276,279,293,174,294,292,295,296,175,298,297,299,289,176,290,288,291,184,274,273,272,275,185,266,264,265,267,183,270,268,269,271,258,180,256,257,259,262,181,260,261,263,253,254,182,252,255,317,319,318,320,200,150,71,201,223,216,245,246,132,151,72,149,111,119,222,219,70,153,121,134,113,68,154,122,135,112,69,152,120,133,74,148,118,110,66,75,146,116,108,64,76,147,117,109,65,145,73,114,218,215,203,197,115,107,67,106,249,241,220,214,313,307,310,308,35,91,19,49,190,20,36,47,191,92,21,90,37,48,189,38,22,94,45,193,39,23,95,46,194,40,24,93,44,192,18,89,42,210,188,207,87,211,34,228,17,88,41,33,187,198,15,196,237,234,243,206,238,205,251,235,86,16,43,186,305,304,316,303,159,140,0,127,28,2,160,128,29,141,1,139,158,126,30,162,4,143,130,27,163,5,144,131,25,161,3,142,129,26,7,138,125,157,32,8,137,124,155,31,6,224,221,156,209,202,10,232,225,236,248,204,247,233,208,250,136,9,123,195,312,314,311,309 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#06e28404eb43925716bfc8e4d73e8cc7ccb918742e903c176b52de636b48f456, 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 22:21:05 · history