Equation 677 Database

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Magma d7511dfee712…

magma d7511dfee712
Size
381
Isomorphism class hash
d7511dfee712cb5c5b2a62f6541b41ff5c53496f9c14f3e2228665b369ad737a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:50:08
Display reorder
380,326,248,296,244,278,240,261,288,265,283,327,284,246,294,245,276,241,263,289,266,247,282,328,295,243,277,242,260,290,264,280,287,251,291,269,256,298,252,323,258,281,285,249,259,292,267,257,299,253,324,279,286,250,262,293,268,255,297,254,325,275,273,271,272,270,274,361,344,343,342,346,362,340,363,345,341,301,127,175,123,140,122,131,170,132,141,322,142,128,176,124,138,120,129,168,133,126,143,315,174,125,139,121,130,169,134,163,167,145,171,158,150,177,149,329,154,164,165,146,155,172,156,151,178,147,302,162,166,144,153,173,157,152,179,148,300,161,159,137,135,136,160,360,359,377,337,330,339,373,372,338,331,307,20,11,16,2,12,21,7,25,3,308,4,18,9,17,1,13,22,8,26,19,5,306,10,15,0,14,23,6,24,59,32,41,33,51,46,37,42,304,50,57,30,39,48,34,52,47,38,43,305,58,31,40,49,35,53,45,36,44,303,54,55,27,28,29,56,348,365,378,332,347,367,366,364,333,349,313,112,103,108,94,107,116,99,117,98,314,96,113,104,109,95,105,114,100,118,111,97,312,102,110,93,106,115,101,119,68,69,78,73,60,86,77,82,310,87,66,70,79,88,74,61,84,75,83,311,67,71,80,89,72,62,85,76,81,309,63,64,91,92,90,65,352,334,375,336,351,374,335,368,350,353,317,180,202,207,193,206,184,198,188,197,318,195,181,203,208,194,204,185,199,186,182,196,316,201,209,192,205,183,200,187,219,223,232,227,214,237,228,236,320,210,220,224,233,211,225,215,238,229,234,321,221,222,231,212,226,213,239,230,235,319,217,218,190,191,189,216,356,354,358,357,376,371,355,379,369,370 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#ee4583ce949a0e270f9516e470f60a7aca92780fb01c370ddec5857db8ff994f, M = {66} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:50:09 · history