Equation 677 Database

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Magma 96bafeedb51f…

magma 96bafeedb51f
Size
321
Isomorphism class hash
96bafeedb51fd8d5cfb251128e2d7ec4ebb8c7093765d0769eec012eb2762c17
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 22:45:50
Display reorder
300,96,244,112,23,128,21,97,245,113,126,243,22,98,111,127,19,99,240,108,131,20,100,241,109,129,18,101,242,110,130,102,250,118,14,123,103,251,119,12,124,104,249,117,13,125,105,246,114,17,122,106,247,115,15,120,107,248,116,16,121,313,312,308,305,269,268,271,228,270,229,273,272,275,274,265,230,264,267,266,231,252,253,255,254,232,256,257,259,258,233,260,261,263,262,293,292,294,234,295,297,296,298,235,299,288,289,291,236,290,276,277,278,237,279,281,280,282,238,283,285,284,286,239,287,320,318,319,317,220,149,134,32,2,30,221,147,132,1,148,31,219,133,0,35,216,145,137,5,33,217,146,135,3,34,218,144,136,4,226,155,140,27,8,227,153,138,28,6,225,154,139,29,7,222,151,143,26,11,223,152,141,24,9,224,150,142,25,10,316,306,307,311,181,157,196,77,171,75,182,158,197,172,156,76,180,195,173,73,184,160,192,170,74,185,161,193,168,72,183,159,194,169,187,163,202,83,177,188,164,203,81,178,186,162,201,82,179,190,166,198,79,176,191,167,199,80,174,189,165,200,78,175,315,302,310,301,41,70,56,85,208,86,39,71,54,209,69,84,40,55,207,88,37,66,59,204,89,38,67,57,205,87,36,68,58,206,47,61,51,91,214,45,62,52,92,215,46,60,53,90,213,43,64,50,94,210,44,65,48,95,211,42,63,49,93,212,314,304,309,303 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, 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 22:45:51 · history